Find the frequency of oscillation given the system In the sy

Find the frequency of oscillation given the system

In the system shown below, the numerical values of m, b and k are given as: m=1 kg, b= 2 N-s/m and k=100N/m. The mass is displaced 0.05m and released without initial velocity. Find the frequency of oscillation.

Solution

Mass, M = 1 kg, Stiffness, K = 100 N/m, Damping coeff, C = 2 N.s/m

Damping ratio = = C/C_c

C_c = 2 x (K x M)

    C_c = 2 X (100 x 1) = 20 N.s/m

Therefore, = C/C_c = 2/20 = 0.1

Natural Frequency of the system, _n = (K / M)

= (100/1) = 10 Hz

Damped Frequency, _d = _n x (1- ²)

= 10 x (1-0.1²)

= 10 x 0.99 = 9.95 Hz