Mechanical Oscillation and Resonance

[mrmonkah]

Homework Statement

A mechanical oscillator system is driven sinusoidally with a force amplitude, F(max). The Oscillator resonates at 27Hz. When driven with the same F(max) at 26Hz or 28Hz, the resulting oscillation has half the amplitude as at resonance. When F(max) is instead applied constantly, the oscillator is displaced by 1mm from its equilibrium position.

What will the oscillators amplitude be when F(max) is applied sinusoidally at resonance?

Homework Equations

\frac{d^{2}x}{dt^{2}} + 2\gamma\frac{dx}{dt} + \omega^{2}x = \frac{1}{m}F_{external}(t)

The Attempt at a Solution

Im finding it difficult to visualise the problem and not so worried about the maths. if you could let me know if i have the right equation in mind, then i can perhaps plug in some numbers a play from there. Other wise i really don't know where to start.

 

[zzzoak]

Your equation differs little from this
http://en.wikipedia.org/wiki/Harmonic_oscillator"