Academia.edu no longer supports Internet Explorer.
To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser .
Enter the email address you signed up with and we'll email you a reset link.
 We're Hiring!
 Help Center
free Damped and Undamped Vibration lab report
Related Papers
Mahmoud Mannaa
Springer eBooks
Eiji Shamoto
Journal of Mechanical Engineering Research
rowland ekeocha
ALFRED SAMPSON
Senthamizh Selven
Saminu Inuwa Bala
Anandakrishnan u
Mohamed Ashraf Sewafy
The Journal of the Acoustical Society of America
Fred Discenzo
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.
RELATED PAPERS
Journal of KONES
Witold Wisniowski
Blaze South
Davorka Šaravanja
Periodica Polytechnica Mechanical Engineering
Emir Neziric
Rainer Massarsch
iJSRED Journal
Hamza Saeed Khan
TJPRC Publication
Applied Sciences
mehmet ilhan
Kingsley Ogunleye
IOP Conference Series: Materials Science and Engineering
Cosmin Mihai Miritoiu
Dr. AJAY KUMAR CHOUBEY
harsha vardhan
Journal of Materials Processing Technology
Huining Wang
International Journal of Innovative Technology and Exploring Engineering
Ganesh Kondhalkar
Chaos, Solitons & Fractals
Grzegorz Litak
Srivatsa Sarat Kumar Sarvepalli
Saeed Alrantisi
15th International Conference on Condition Monitoring and Machinery Failure Prevention Technologies, CM 2018/MFPT 2018
Naumenko Alex
IOSR Journals
 We're Hiring!
 Help Center
 Find new research papers in:
 Health Sciences
 Earth Sciences
 Cognitive Science
 Mathematics
 Computer Science
 Academia ©2024
Vibration Experiments
 First Online: 23 February 2023
Cite this chapter
 C. Sujatha 2
This chapter describes seventeen fundamental experiments in vibration which can easily be conducted in the laboratory to understand the basic vibration theory which has been described in Chapter 2. The presentation is such that an academician can mix and match these experiments to suit the laboratory courses being taught at undergraduate or postgraduate levels. The material will also be useful for researchers who would like to set up basic experiments in the laboratory. Simple rigs that can easily be fabricated in the workshop for specific experiments are suggested. The description of every experiment starts with the aim, theory behind the experiment, test setup and procedure, as well as how to report the results. Suggestions are given for the choice of transducers (described in Chapter 3) and for alternate experimental setups.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Subscribe and save.
 Get 10 units per month
 Download Article/Chapter or eBook
 1 Unit = 1 Article or 1 Chapter
 Cancel anytime
 Available as PDF
 Read on any device
 Instant download
 Own it forever
 Available as EPUB and PDF
 Compact, lightweight edition
 Dispatched in 3 to 5 business days
 Free shipping worldwide  see info
 Durable hardcover edition
Tax calculation will be finalised at checkout
Purchases are for personal use only
Institutional subscriptions
Bibliography
Beckwith, T. G., Marangoni, R. D., & Lienhard, J. H. (1993). Mechanical measurements . US: Pearson Education.
Google Scholar
Brandt, A. (2011). Noise and vibration analysis: Signal analysis and experimental procedures . Wiley.
Buzdugan, Gh., Mih \(\breve{\rm a}\) ilescu, E., & Rades M. (1986). Vibration measurement (mechanics: Dynamical systems) . Netherland: Springer.
Collacott, R. A. (1979). Vibration monitoring and diagnosis . London: George Godwin Ltd.
Crocker, M. J. (2007). Handbook of noise and vibration control . New York: McGrawHill.
Book MATH Google Scholar
Figliola, R. S., & Beasley, D. E. (2014). Theory and design for mechanical measurements . Wiley.
Goldman, S. (1999). Vibration spectrum analysis: A practical approach . Industrial Press Inc.
Inman, D. J. (1989). Vibration: With control, measurement, and stability . Pearson College Div.
McConnell, K. G., & Varoto, P. S. (1995). Vibration testing: Theory and practice . New York: WileyIEEE.
Nakra, B. C., & Chaudhry, K. K. (2016). Instrumentation, measurement and analysis . McGrawHill Education India Private Limited.
Piersol, A. G. (2002). Harris’ shock and vibration handbook . McGrawHill Professional, eBook.
Piersol, A., & Paez, T. (2009). Harris’ shock and vibration handbook (McGrawHill Handbooks), McGrawHill Education.
Scheffer, C., & Girdhar, P. (2004). Practical machinery vibration analysis and predictive maintenance (practical professional) . Newnes.
Sinha, J. K. (2014). Vibration analysis, instruments, and signal processing . CRC Press.
Smith, J. D. (1989). Vibration measurement and analysis . London: Butterworth.
Sujatha, C. (2010). Vibration and acoustics: Measurement and signal analysis . Tata McGrawHill Education.
Wowk, V. (1991). Machinery vibration: Measurement and analysis . McGrawHill Education.
Venkateshan, S. P. (2008). Mechanical measurements . ANE Books India, and CRC Press.
Download references
Author information
Authors and affiliations.
Department of Mechanical Engineering, IIT Madras, Chennai, India
You can also search for this author in PubMed Google Scholar
Corresponding author
Correspondence to C. Sujatha .
Rights and permissions
Reprints and permissions
Copyright information
© 2023 The Author(s)
About this chapter
Sujatha, C. (2023). Vibration Experiments. In: Vibration, Acoustics and Strain Measurement. Springer, Cham. https://doi.org/10.1007/9783031039683_10
Download citation
DOI : https://doi.org/10.1007/9783031039683_10
Published : 23 February 2023
Publisher Name : Springer, Cham
Print ISBN : 9783031039676
Online ISBN : 9783031039683
eBook Packages : Engineering Engineering (R0)
Share this chapter
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt contentsharing initiative
 Publish with us
Policies and ethics
 Find a journal
 Track your research
5.2 Free vibration of conservative, single degree of freedom, linear systems.
First, we will explain what is meant by the title of this section.
It turns out that all 1DOF, linear conservative systems behave in exactly the same way. By analyzing the motion of one representative system, we can learn about all others.
We will follow standard procedure, and use a springmass system as our representative example.
There is a standard approach to solving problems like this
(i) Get a differential equation for s using F=ma (or other methods to be discussed)
(ii) Solve the differential equation.
The picture shows a free body diagram for the mass.
Newton’s law of motion states that
This is our equation of motion for s .
5.2.1 How to solve equations of motion for vibration problems
Note that all vibrations problems have similar equations of motion. Consequently, we can just solve the equation once, record the solution, and use it to solve any vibration problem we might be interested in. The procedure to solve any vibration problem is:
1. Derive the equation of motion, using Newton’s laws (or sometimes you can use energy methods, as discussed in Section 5.3)
2. Do some algebra to arrange the equation of motion into a standard form
3. Look up the solution to this standard form in a table of solutions to vibration problems.
We have provided a table of standard solutions as a separate document that you can download and print for future reference.
We will illustrate the procedure using many examples.
5.2.2 Solution to the equation of motion for an undamped springmass system
We would like to solve
We therefore consult our list of solutions to differential equations, and observe that it gives the solution to the following equation
Finally, we see that if we define
then our equation is equivalent to the standard one.
The solution for x is
When we present the solution, we have a choice of writing down the solution for x, and giving formulas for the various terms in the solution (this is what is usually done):
Alternatively, we can express all the variables in the standard solution in terms of s
But this solution looks very messy (more like the Mathematica solution).
Observe that:
5.2.3 Natural Frequencies and Mode Shapes.
We saw that the spring mass system described in the preceding section likes to vibrate at a characteristic frequency, known as its natural frequency. This turns out to be a property of all stable mechanical systems.
All stable, unforced, mechanical systems vibrate harmonically at certain discrete frequencies, known as natural frequencies of the system.
A system with three masses would have three natural frequencies, and so on.
In general, a system with more than one natural frequency will not vibrate harmonically.
For example, suppose we start the two mass system vibrating, with initial conditions
In general, the vibration response will look complicated, and is not harmonic. The animation above shows a typical example (if you are using the pdf version of these notes the animation will not work  you can download the matlab code that creates this animation here and run it for yourself)
then the response is simply
i.e., both masses vibrate harmonically, at the first natural frequency, as shown in the animation to the right. (To repeat this in the MATLAB code, edit the file to set A1=0.3 and A2=0)
Similarly, if we choose
i.e., the system vibrates harmonically, at the second natural frequency. (To repeat this in the MATLAB code, edit the file to set A2=0.3 and A1 = 0)
The special initial displacements of a system that cause it to vibrate harmonically are called `mode shapes’ for the system.
If a system has several natural frequencies, there is a corresponding mode of vibration for each natural frequency.
The natural frequencies are arguably the single most important property of any mechanical system . This is because, as we shall see, the natural frequencies coincide (almost) with the system’s resonant frequencies . That is to say, if you apply a time varying force to the system, and choose the frequency of the force to be equal to one of the natural frequencies, you will observe very large amplitude vibrations.
When designing a structure or component, you generally want to control its natural vibration frequencies very carefully. For example, if you wish to stop a system from vibrating, you need to make sure that all its natural frequencies are much greater than the expected frequency of any forces that are likely to act on the structure. If you are designing a vibration isolation platform, you generally want to make its natural frequency much lower than the vibration frequency of the floor that it will stand on. Design codes usually specify allowable ranges for natural frequencies of structures and components.
Once a prototype has been built, it is usual to measure the natural frequencies and mode shapes for a system. This is done by attaching a number of accelerometers to the system, and then hitting it with a hammer (this is usually a regular rubber tipped hammer, which might be instrumented to measure the impulse exerted by the hammer during the impact). By trial and error, one can find a spot to hit the device so as to excite each mode of vibration independent of any other. You can tell when you have found such a spot, because the whole system vibrates harmonically. The natural frequency and mode shape of each vibration mode is then determined from the accelerometer readings.
5.2.4 Calculating the number of degrees of freedom (and natural frequencies) of a system
When you analyze the behavior a system, it is helpful to know ahead of time how many vibration frequencies you will need to calculate. There are various ways to do this. Here are some rules that you can apply:
The number of degrees of freedom is equal to the number of independent coordinates required to describe the motion . This is only helpful if you can see by inspection how to describe your system. For the springmass system in the preceding section, we know that the mass can only move in one direction, and so specifying the length of the spring s will completely determine the motion of the system. The system therefore has one degree of freedom, and one vibration frequency. Section 5.6 provides several more examples where it is fairly obvious that the system has one degree of freedom.
For a 2D system, the number of degrees of freedom can be calculated from the equation
p is the number of particles in the system
To be able to apply this formula you need to know how many constraints appear in the problem. Constraints are imposed by things like rigid links, or contacts with rigid walls, which force the system to move in a particular way. The numbers of constraints associated with various types of 2D connections are listed in the table below. Notice that the number of constraints is always equal to the number of reaction forces you need to draw on an FBD to represent the joint
1 constraint (prevents motion in one direction) 

(if the link has mass, it should be represented as a rigid body)
1 constraint (prevents relative motion parallel to link)


(two bodies meet at a point)
1 constraint (prevents interpenetration)
2 constraints (prevents relative motion 

(two rigid bodies meet along a line)
2 constraint (prevents interpenetration and rotation)
3 constraints (prevents relative motion) 

(generally only applied to a rigid body, as it would stop a particle moving completely)
2 constraints (prevents motion horizontally and vertically) 

(rare in dynamics problems, as it prevents motion completely)
Can only be applied to a rigid body, not a particle
3 constraints (prevents motion horizontally, vertically and prevents rotation) 

For a 3D system, the number of degrees of freedom can be calculated from the equation
where the symbols have the same meaning as for a 2D system. A table of various constraints for 3D problems is given below.
(5 constraints 

(5 constraints 

(4 constraints 

4 constraints (prevents all motion, prevents rotation about 1 axis) 

3 constraints 

(two rigid bodies meet at a point)
1 constraint (prevents interpenetration)
3 constraints, possibly 4 if friction is sufficient to prevent spin at contact) 

(two rigid bodies meet over a surface)
3 constraints: prevents interpenetration and rotation about two axes.
6 constraints: prevents all relative motion and rotation. 

(rare in dynamics problems, as it prevents all motion)
6 constraints (prevents all motion and rotation) 

5.2.4 Calculating natural frequencies for 1DOF conservative systems
In light of the discussion in the preceding section, we clearly need some way to calculate natural frequencies for mechanical systems. We do not have time in this course to discuss more than the very simplest mechanical systems. We will therefore show you some tricks for calculating natural frequencies of 1DOF, conservative, systems. It is best to do this by means of examples.
Our first objective is to get an equation of motion for s . We could do this by drawing a FBD, writing down Newton’s law, and looking at its components. However, for 1DOF systems it turns out that we can derive the EOM very quickly using the kinetic and potential energy of the system.
The potential energy and kinetic energy can be written down as:
Differentiate our expressions for T and V (use the chain rule) to see that
Finally, we must turn this equation of motion into one of the standard solutions to vibration equations.
Our equation looks very similar to
and substitute into the equation of motion:
By comparing this with our equation we see that the natural frequency of vibration is
Summary of procedure for calculating natural frequencies:
(1) Describe the motion of the system, using a single scalar variable (In the example, we chose to describe motion using the distance s );
(2) Write down the potential energy V and kinetic energy T of the system in terms of the scalar variable;
(4) Arrange the equation of motion in standard form;
(5) Read off the natural frequency by comparing your equation to the standard form.
Example 2: A nonlinear system.
Find the natural frequency of vibration for a pendulum, shown in the figure.
We will idealize the mass as a particle, to keep things simple.
We will follow the steps outlined earlier:
(2) We write down T and V :
(3) Differentiate with respect to time :
(i) Find the static equilibrium configuration(s) for the system .
(ii) Assume that the system vibrates with small amplitude about a static equilibrium configuration of interest.
(iii) Linearize the equation of motion, by expanding all nonlinear terms as Taylor Maclaurin series about the equilibrium configuration.
Now, recall the TaylorMaclaurin series expansion of a function f(x) has the form
Apply this to the nonlinear term in our equation of motion
Finally, we can substitute back into our equation of motion, to obtain
(iv) Compare the linear equation with the standard form to deduce the natural frequency.
We can do this for each equilibrium configuration.
Next, try the remaining static equilibrium configuration
If we look up this equation in our list of standard solutions, we find it does not have a harmonic solution. Instead, the solution is
No wonder the equation is predicting an instability…
Here is a question to think about. Our solution predicts that both x and dx/dt become infinitely large. We know that a real pendulum would never rotate with infinite angular velocity. What has gone wrong?
We follow the same procedure as before.
The potential and kinetic energies of the system are
Now, expand all the nonlinear terms (it is OK to do them one at a time and then multiply everything out. You can always throw away all powers of x greater than one as you do so)
If you prefer, you can use Mathematica to do the Taylor series expansion:
(The number 4 in the ‘series’ command specifies the highest power of x that should appear in the expansion). We now have an equation in standard form, and can read off the natural frequency
Our first objective is to get an equation of motion for s . We do this by writing down the potential and kinetic energies of the system in terms of s .
The potential energy is easy:
The first term represents the energy in the spring, while second term accounts for the gravitational potential energy.
The kinetic energy is slightly more tricky. Note that the magnitude of the angular velocity of the disk is related to the magnitude of its translational velocity by
Thus, the combined rotational and translational kinetic energy follows as
Now, note that since our system is conservative
Differentiate our expressions for T and V to see that
This is now in the form
and by comparing this with our equation we see that the natural frequency of vibration is
IMAGES
VIDEO
COMMENTS
The free vibration experiment is a common experimental technique used in mechanical engineering to determine the natural frequency of a springmass system without damping. A mass is suspended from a spring, displaced from its equilibrium position, and the ensuing oscillation is recorded using a displacement transducer.
This is a Premium Document. Some documents on Studocu are Premium. Upgrade to Premium to unlock it. Dynamics Lab sheet 1  Free Vibration Experiment  PKP. Course: lab strength (mec424) 108Documents. Students shared 108 documents in this course. University: Universiti Teknologi MARA. AI Chat.
Lab Sheet No : 1 Title : Free Vibration Experiment  Natural Frequency Of Spring Mass System Without Damping. 1 Introduction. Free vibration is vibration that takes place when a system oscillates under the action of forces inherent in the system itself.
2.3) Free Vibration with viscous damping system 2.4) Damping ratio determination (Logarithmic decrement method) 3. Forced vibration of single degree of freedom ... Assignment A written report / work out vibration problems aims for the student to acquire understanding the measurements of natural frequency, amplitude of
MECHANICAL VIBRATIONS. Course Code. MEM582. MQF Credit. 3. Course Description. The course emphasizes understanding of the fundamental concepts of vibrations. It begins with free vibration of singledegreeoffreedom for undamped and damped systems followed by forced vibration with harmonic excitation. Multidegreeoffreedom systems, equations ...
Experiment lab report for Free Vibration Experiment  Natural Frequenc... View more. Course. Static and Dinamic (BFC 10103) 8 Documents. Students shared 8 documents in this course. University Universiti Tun Hussein Onn Malaysia. Academic year: 2020/2021. Uploaded by: Anonymous Student.
2 LAB 1: FREE VIBRATION Part I. Displacement 1.2. Experiment A.  Free oscillations of a springmass system Goals: The goal of this experiment is to determine the mass of the cart and compare the experimental and theoretical natural frequencies. (1)Disconnect the damper from the cart and make sure it will not interfere with the movement of the ...
In this lab, the oscilloscope was used to determine the sinusoidal wave (amplitude) of the damped and undamped vibrations of the spring fEXPERIMENTAL METHOD/PROCEDURE i.TEST 1 2. One or two available masses was placed in the tube which formed the pendulum arm, and the screw was tightened 3. The damper arm was detached if already connected 4.
Modal analysis with roving impact and fixed transducer. This chapter describes seventeen basic vibration experiments which can be conducted in the laboratory to understand the basic vibration theory described in Chap. 2. Suggestions are given for the choice of transducers or alternate experimental setups.
DYNAMIC LAB 3 Forced Vibration Experiment; Torsion Test LAB Report; Torsion TEST lab 3 strenght lab; MEC 424  Laboratory 1  LAB; Natural Frequency Of Spring Mass System Without Damping; ... MEC 424  LABORATORY REPORT. TITLE : FREE VIBRATION EXPERIMENTNATURAL FREQUENCY OF SPRING MASS SYSTEM WITHOUT DAMPING.
5.2 Free vibration of conservative, single degree of freedom, linear systems. First, we will explain what is meant by the title of this section. Recall that a system is conservative if energy is conserved, i.e. potential energy + kinetic energy = constant during motion. Free vibration means that no time varying external forces act on the system.
Free Vibration 1.1 Theory 1.1.1 Free Vibration, Undamped Consider a body of mass msupported by a spring of sti ness k, which has negligible inertia (Figure 1.1). Let the mass mbe given a downward displacement from the static equilibrium position and released. At some time tthe mass will be at a distance xfrom the equilibrium position and the
The laboratory experiments that were developed include the study of free vibra tion, forced vibration, 1 DOF, 2DOF, and 3 DOF systems, dynamic absorber, modes of vibratio n, and the effects of damping. In this paper, only the free vibration experiments, four in a ll, will be described in detail, as well
dynamic lab report mec424 mec mechanics lab dynamics forced vibration resonance of spring dashpot system with spring title force vibration experiment resonance. Skip to document. University; High School; Books; Discovery. ... Free body diagram of the beam. Experiment 1: Without damper Frequency, f (Hz) 2 x Amplitude, 2a (cm) Amplitude, a (cm) 5 ...
DEPARTMENT OF MECHANICAL ENGINEERING. LAB MANUAL. SUBJECT: MECHANICAL VIBRATION. B.TECH 7thSemester BRANCH:  ME KCT COLLEGE OF ENGG & TECH, FATEHGARH Punjab Technical University. KCT COLLEGE OF ENGG. & TECH DEPARTMENT OF ME MECHANICAL VIBRATION. LIST OF EXPERIMENTS. 1. To verify the relation of simple pendulum.