Simple Harmonic Motion - Finding max speed of an oscillator

[KEØM]

Homework Statement

A 300g oscillator has a speed of 95.4 cm/s when its displacement is 3.0 cm and 71.4 cm/s when it displacement is 6.0 cm. What is the oscillator's maximum speed?

Homework Equations

x = Acos($$\omega$$t + $$\phi$$)
v = -$$\omega$$Asin($$\omega$$t + $$\phi$$)
vmax = $$\omega$$A
v = $$\omega$$(A^2 - x^2)^1/2

The Attempt at a Solution

I manipulated the fourth equation into

$$\omega$$A or vmax = (v^2 + (x$$\omega$$)^2)^1/2

so if I get $$\omega$$ from somewhere else then I can use it to solve it for vmax but I can't see a way of doing that with the given info.

 

[horatio89]

Hmm... the fact that the mass is given gives me an idea. Try approaching the question from the conservation of energy, where E_tot = 1/2 mv² + 1/2 kx². Equate E_tot of the two cases would solve for k, and then one could find the value of E_tot.

The next step is fairly simple: at maximum speed, E_tot = 1/2mv_max²

 

[KEØM]

Thank you very much for your help.

For a value of k I got 44.48 N/m

and for E$$_{}tot$$ I got about .157J

and then solving for v$$_{}max$$ I got 1.022 m/s or 102.2 cm/s which makes sense.

Thanks again for your help.

KE0M