Assignment:
Question 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
Question 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
Question 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
Question 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
Question 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
Question 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
Question 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
Question 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
Question 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
Question 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