# Simple Harmonic Motion - Finding max speed of an oscillator

1. Nov 29, 2008

### KEØM

1. The problem statement, all variables and given/known data
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?

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

3. 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.

2. Nov 29, 2008

### horatio89

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

The next step is fairly simple: at maximum speed, Etot = 1/2mvmax2

3. Nov 29, 2008

### 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.