Simple Harmonic Motion using total mechanical energy

[StrawHat]

Homework Statement

A 250 gram mass is connected to a spring and executes simple harmonic motion. The period of motion is 0.5 seconds and the total mechanical energy is 0.50J. What is the amplitude of motion?

Homework Equations

ΔU = 1/2kx²

The Attempt at a Solution

I get

1/2kx² = 0.5J,

then I get

kx² = 1.0J

Not sure where to go from here. I do have the answer from the answer key, but I have no idea how to actually get the answer. I think I'm supposed to integrate something, but I'm not sure how to incorporate the time value into any equations.

 

[NoPoke]

do you know another equation involving k that applies to your situation?

 

[StrawHat]

kx=ma, perhaps? If so, should I use kx = m(dv/dt)? But then how will I obtain a value for velocity?

 

[NoPoke]

what does the solution of the differential equation kx=ma look like? [Check your notes on simple harmonic motion, watch out for sign conventions]

 

[StrawHat]

d/dt(kx)=d/dt(ma)
k(dx/dt)=m(da/dt)
kv(t)=m(da/dt)?

 

[NoPoke]

a = dv/dt = d2x/dt2 would be a better route. da/dt is going in the wrong direction.

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the solution will be of the form x = F(t) where F will be a function that you recognise.

 

[StrawHat]

x=ma/k? I am totally lost...

I have ax=4. Am I on the right track?

 

[NoPoke]

what do your notes say for how x varies in a system that is executing simple harmonic motion? There is something not quite right with your kx = ma. Not quite because it is normally expressed in an ever so slightly different way.

 

[StrawHat]

F = -kx
W = Fd =∫F_netdx
W_total = ΔK
ΔU = 1/2kx²

 

[NoPoke]

If y = sin(t) what is dy/dt, what about d2y/dt2

 

[StrawHat]

dy/dt=cos(t), d2y/dt2=-sin(t)?

Thank you for your help thus far, but it's 4AM over here in the EST timezone, so I must go to bed. I will check back on this thread in five hours or so.

 

[NoPoke]

so how are y and d2y/dt2 related? is there anything that you have posted so far that looks similar?

 

[StrawHat]

m(dv/dt)=k(dx/dt)
m(dv/dt)=kv?