Question

A driving force of the form F(t) = (0.212 N) sin (2xft) acts on a weakly damped spring oscillator with mass 6.98 kg, spring constant 362 N/m, and damping constant 0.261 kg/s. What frequency fo of the driving force will maximize the response of the oscillator? fo = Hz Find the amplitude Ao of the oscillator's steady-state motion when the driving force has this frequency

Answer 1

Sol::

Given data:
F(t) = (0.212 N) sin (2π*f*t)

mass(m)= 6.98 kg,
spring constant(k)= 362 N/m
damping constant = 0.261 kg/s

A)

So as we have frequency
f=(1/2π)√(k/m)
= 0.1591*√(362/6.98)
= 1.15 Hz

B)

Now by using the formula

A_0 = (F_0/b)*√(m/k)
= (0.212/0.261)* √(6.98/362)
= 0.0157 m

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