I just need the oscillators damping constant Engineers can determine properties

Question

I just need the oscillators damping constant

Engineers can determine properties of a structure that is modeled as damped spring oscillator-such as a bridge-by applying a driving force to it. A weakly damped spring oscillator of mass 0.236 kg is driven by a sinusoidal force at the oscillator's resonance frequency of 21.9 Hz. Find the value of the spring constant. The amplitude of the driving force is 0.424 N and the amplitude of the oscillator's steady-state motion in response to this driving force is 0.845 m. What is the oscillator's damping constant?

Explanation / Answer

m = 0.236 kg

k = 4468.8 N/m

driving force, Focoswt

F = 0.424N and w = 2*pi*21.9 rad/s

steady state amplitude = 0.845m

c = damping constant/ 2*sqrt(km)

damping constant,f = 2*c*sqrt(km)

= c*64.948

we have to find f, dampind constant

steady state amp. = Fo/k / sqrt (1 - w^2/wn^2)^2 + (2cw/wn)^2)

wn = sqrt(k/m)

= 137.602 rad/s

w = 2*pi*21.9

= 137.602

since w = wn

steady state amp = Fo/k) / (2c)

0.845 = 0.424/ (2*4468.48 *c)

c = 5.615 *10^-5

damping constant = 3.647 *10^-3 kg./s

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