PES INSTITUTE OF TECHNOLOGY BANGALORE – SOUTH CAMPUS Hosur Road, (1K.M. Before Electronic City), Bangalore – 560 100

DEPARTMENT OF MECHANICAL ENGINEERING

SCHEME AND SOLUTION – I INTERNAL TEST

Subject : MECHANICAL VIBRATIONS

Semester : VII

Sub. Code : 10ME72 Section: A, B, C

Name of the faculty : Dr. RB/SP/SC

Q.No Marks

1 A body is subjected to harmonic motions x1=10 sin (ωt + 300) and x2=5 cos (ωt + 600). What

harmonic motion should be given to the body to bring it to equilibrium?

Solution :

10

2

Add the following harmonics analytically and check the solution graphically.

x1=3 sin (ωt + 300)

x2=4 cos (ωt + 100)

Solution :

10

3

Derive an equation for work done by harmonic force.

Solution :

10

4

Define the following terms

i) Simple harmonic motion ; ii) Resonance ; iii) Degree of freedom ; iv) Damping ;

v) Natural frequency

Answer :

i) Simple Harmonic Motion

10

ii) Resonance

iii) Degree of Freedom

5

iv) Natural Frequency

When a body is provided an initial displacement and released, it performs free vibrations on its

own. The frequency with which it performs free vibrations is called a natural frequency. It is a

principal characteristic of the system. A body with ‘n’ degrees of freedom has ‘n’ no. of natural

frequencies and ‘n’ no. of mode shapes associated with them. Determination of natural

frequencies is highly important as resonance occurs when the frequency components in external

excitataion matches with one of the natural frequencies of the system.

Represent the periodic motion given in the fig. Q5 by harmonic series

10

Fig. Q5

Solution :

6

Derive the natural frequency of a spring mass system, where the mass of the spring is also to be

taken into account.

10

7

Derive the natural frequency of undamped torsional vibration

Solution :

10

8

Determine the natural frequency of simple pendulum

i) Neglecting the mass of the rod

ii) Considering the mass of the rod

Solution :

i) Neglecting the mass of the rod