# Vibrations problems

1) If the complex number 5+2i is expressed in the exponential form Ae^io, determine the values of A and O.

a)3.3754, 32.70

b)4.6483, 27.50

c)5.3852, 21.80

d)6.6722, 15.55

2) A harmonic motion has an amplitude of 0.05m and a frequency of 10Hz. Determine the maximum velocity.

a)1.571m/s

b)3.142m/s

c)4.672m/s

d)6.284m/s

3) A harmonic motion has an amplitude of 0.05m and a frequency of 10Hz. Determine the maximum acceleration.

a)62.8m/s^2

b)98.6m/s^2

c)134.5m/s^2

d)197.4m/s^2

4) A Mass-Spring-Damper system is tested to determine the value of the viscous damping coefficient C. Assume k=150N/m and m=30kg. The vibrational amplitude is observed to decrease 33% of its initial value after two consecutive cycles. What is the logarithmic decrement?

a)0.6931

b)0.8047

c)0.5543

5) A Mass-Spring-Damper system is tested to determine the value of the viscous damping coefficient C. Assume k=150N/m and m=30kg. The vibrational amplitude is observed to decrease 33% of its initial value after two consecutive cycles. What is the value of the viscous damping ratio?

a)0.0637

b)0.0870

c)0.0992

6) A Mass-Spring-Damper system is tested to determine the value of the viscous damping coefficient C. Assume k=150N/m and m=30kg. The vibrational amplitude is observed to decrease 33% of its initial value after two consecutive cycles. What is the value of the viscous damping coefficient C?

a)40.23 Ns/m

b)30.11 Ns/m

c)11.67 Ns/m

7) A spring-mass system with m=10kg and k=5000 N/m is subjected to a harmonic force having an amplitude of 250 N. If the maximum amplitude of the mass is observed to be 100mm, find the value of the forcing frequency in rad/s.

a)15.8 rad/s

b)22.4 rad/s

c028.6 rad/s

8) The magnification factor of an undamped spring mass system is infinite when the frequency ratio has a value of 1.1. True or False?

a)True

b)False

9) In a damped spring mass system the maximum amplitude always occurs at a frequency ratio of r=1.0. True or False?

a)True

b)False

10) For a two degree of freedom system with damping, it is possible to choose a system of coordinates q1(t) and q2(t) which give you equations of motion that are uncoupled both statically and dynamically. True or False?

a)True

b)False

#### Solution Summary

This answers several questions related to vibration physics problems.