First Year Forced Oscillator Problem

[Eugene Kelly]

Homework Statement

Damping is negligible for a 0.164 kg mass hanging from a light 6.70 N/m spring. The system is driven by a force oscillating with an amplitude of 1.77 N. At what frequency will the force make the mass vibrate with an amplitude of 0.500 m? There are two possible solutions, enter one of them.

Homework Equations

I think I have too use A=(F/m)/((w^2-w0^2)^2+(bw/m)^2)^1/2 where w is omega.

The Attempt at a Solution

The problem I am having is understanding this equation because b is not given and I do not know what that different angular frequencies stand for or if I can use w=(k/m)^1/2. Solving it isn't a problem I just can't understand the equation, my prof did a terrible time explaining it and my text isn't making sense too me. Thank you too whomever in advance.

 

[haruspex]

Not an area I've ever studied, but if I compare the innards of your equation with that at http://en.wikipedia.org/wiki/Harmonic_oscillator#Driven_harmonic_oscillators,
it seems that $b = 2m\omega_0\zeta$. But your problem says no damping, so $\zeta$ should be zero, no?

 

[rude man]

1. Either solve the ODE for displacement amplitude with zero damping and a forcing function of F(t) = A sin(wt), or look it up in your textbook or elsewhere. This is a 2nd order linear ODE with a forcing function and no initial conditions. Solve the usual way, or look the answer up in your textbook or elsewhere.
2. That gives you amplitude as a function of F,m,k and w (w=2 pi f). Set this to the given amplitude.
3. Solve for w. Note that there are two possible answers for w since A can be either + or - . What do the two frequencies correspond to in terms of the physics of the problem?