acts on a weakly damped spring oscillator with mass 6.65 kg, spring constant 322

Question

acts on a weakly damped spring oscillator with mass 6.65 kg, spring constant 322 N/m, and damping constant 0.213 kg/s. What frequency of the driving force will maximize the response of the oscillator?

Find the amplitude of the oscillator's steady-state motion when the driving force has this frequency.

A driving force of the form F(t)= (0.250 N)sin(2pi/ft) acts on a weekly damped spring oscillator with mass 6.65 kg, spring constant 322 N/m, and damping constant 0.213 kg/s. What frequency of the driving force will maximize the response of the oscillator? Find the amplitude of the oscillator's steady-state motion when the driving force has this frequency.

Explanation / Answer

frequency for which response is maximum.

n = nf

nf = 1/2pi *sqrt(k/m)

= 1.107 Hz

amplitude = Fo/k/ (2s)

s = 0.213/2*sqrt(km)

= 2.301 *10^-3

amplitude = Fo/ (2*322*2.301*10^-3)

= 0.169 m

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