2 A damped springmass system has W 2 lb k 4 lbin and an un

2. A damped spring-mass system has W = 2 lb., k = 4 lb/in, and an unknown damping constant. If amplitude measurements show a decay rate of 10 percent per cycle, determine the value of the damping constant.

Solution

A damped spring-mass system has W = 2 lb., k = 4 lb/in, and an unknown damping constant. If amplitude measurements show a decay rate of 10 percent per cycle, determine the value of the damping constant

A spring-mass system with m=10 kg and k = 5000 N/m is subjected to a harmonic force of amplitude 250 N and frequency . If the maximum amplitude of the mass is observed to be 100 mm, find the value of driving frequency in Hz.
Ans:

n = k / m

= 5000 /10 = 22.3607 rad/s

st = F0/ k = 250 /5000 = 0.05m

X = st (1/(1. ( /n )2 )
1/2 1/2

i.e. = n (1. st / X ) = 22.3607(1. 0.05/ 0.10) = 15.8114 rad/s ..._(rad/s)
f = 15.8114/(2) = 2.52 Hz