Oscillatory motion

map7s

There is a displacement versus time graph of a 3.4 g mass on a spring that is in oscillatory motion. A=0.5 and the wavelength for one period is 3 s while the total time shown on the graph is 7 s. I need to find out the maximum speed of this mass.

At first I thought that it would easily be the amplitude divided by the time at that highest amplitude, but obviously that was wrong. I then decided to try energy conservation, which I think is right, but I think that I am not using the correct equation. I've been trying to do some form of mgh=1/2 mv^2 and solving for v. I changed h to x and I knew that x=Acos((2pi/T)t) so I put that in for h and I tried to solve for v. I plugged in my answer and it was wrong, so I'm pretty sure that I just didn't use a correct form of this equation. How can I get a more appropriate form of this equation to use (if it is indeed the correct method) ?

OlderDan

If this is a calculus based course, you know the velocity is the derivative of the displacement. If you can write x(t) you can find v(t). If it is not calculus based, almost surey your text gives you the equations for displacement, velocity, and acceleration of a harmonic oscillator as a function of time. From the graph you can find the things you need to use those equations.