Maximum Speed Formula for Simple Harmonic Motion

[roughneck84]

I have been torturing myself with this problem for a couple weeks now and I am stumped. The unit I am working on is called simple harmonics. The question is:
Prove that the maximum speed (Vmax) of a mass on a spring is given by 2(pi)fA
I am guessing that the question wants me to re-arrange one of the formulas that was learned in this chapter but i am just lost.

Here are the formulas related to this unit.
Fx = -kx , W=1/2kx^2, T=[2(pi)r] / v , Et = 1/2mv^2 + 1/2kx^2, f = 1/2(pi) sq_rt(k/m)
or f = 1/2(pi) sq_rt a/-x

Please any help would be greatly appreciated

 

[G01]

OK. First off are you in a calculus based course? I ask because this can be proved in one to two lines with calculus.

 

[roughneck84]

somewhat. we learned trigonomic method. cosine law and pathagorean theorem

 

[roughneck84]

anyone ??

 

[G01]

Do you know how to take a derivative?

If not, then try starting the problem this way:

Start with your energy equation:

Et = 1/2mv^2 + 1/2kx^2

First, try to get Et in terms of the wave's amplitude.

After this, fill in all the information for when v=v_max. Can you take it from here? If not, show me how far you can get.