Forced Oscillations?

Question

Damping is negligible for a 0.150kg object hanging from a light 6.30N/m spring. A sinusoidal force with an amplitude of 1.70N drives the system. At what frequency will the force make the object vibrate with an amplitude of 0.440m?

Answer 1

For a negligibly-damped system, the steady-state response is
A = (f/m) / |(w0^2-w^2)|
where w0 = natural frequency and w = forcing frequency. (This is a simplification of the with-damping equation in the ref.)
Solving,
w^2 = w0^2 ± (f/m)/A
w1 = sqrt(w0^2 - (f/m)/A)
w2 = sqrt(w0^2 + (f/m)/A)
For this system,
w0^2 = k/m = 42 rad^2/s^2 = s^-2
(f/m)/A = 25.7576 ms^-2/m = s^-2
w1 = 4.0302 rad/s
w2 = 8.2315 rad/s