PES SCHOOL OF ENGINEERINGPES INSTITUTE OF TECHNOLOGY BANGALORE – SOUTH CAMPUS Hosur Road, (1K.M. Before Electronic City), Bangalore – 560 100
DEPARTMENT OF MECHANICAL ENGINEERING
Subject : MECHANICAL VIBRATIONS
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
Solution :
10
4
Define the following terms
i) Simple harmonic motion ; ii) Resonance ; iii) Degree of freedom ; iv) Damping ;
v) Natural frequency
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
Solution :
6
Derive the natural frequency of a spring mass system, where the mass of the spring is also to be
taken into account.
Solution :
10
8
Solution :