Homework question concerning simple harmonic motion

[robf224]

Homework Statement

A system has a period of 3 seconds. The 4 kg mass oscillates with an amplitude of 0.7 meters. At what position is 50% of its energy in the form of kinetic energy and what is its velocity then?

Homework Equations

work = Potential energy + Kinetic energy
(1/2)kA^2 = (1/2)kx^2 + (1/2)mv^2

The Attempt at a Solution

I found k = 17.55 Newton meters.
So, I was thinking of two possible approaches:
a.) (1/2)kA^2 - (1/2)kx^2 = (1/2)mv^2
b.) kx^2 = mv^2

I'm pretty sure I'd use my second idea. If that's right, what would I plug in for x? The amplitude?

 

[Poop-Loops]

Yes, you are correct to use kx^2 = mv^2. Your term 0.5kA^2 is the same thing as 0.5kx^2, the only difference is that "amplitude" can mean more than 1 direction.

So for example if your mass could go in either the X or Y direction, 0.5kA^2 = 0.5kx^2 + 0.5ky^2

So just use option B.

 

[alphysicist]

Hi robf224,

I don't think you should use either of your two equations separately. The first equation contains the total energy, and the second has the 50% condition. But you now have two equations with two unknowns and can solve the two equations simultaneously to find both x and v.