Help Solve Physics Problem: Find Max Displacement w/ Speed & Spring Constant

[punjabi_monster]

An object vibrates at the end of a horizontal spring (k=955 N/m) along a frictionless surface. The speed of the object is 0.250 m/s when its displacement is 0.145 m. What is the maximum displacement of the object if its maximum speed is 0.322 m/s?

I understand to find max displacement, you use the formula:
Et=1/2kA^2

Now that you have to find Et, you can't use teh formula Et=1/2mvo^2. or can't find Ek, as you don't have the mass.

Can someone please tell me how to find Et. tahnks.

 

[Sirus]

If by Et you mean total energy...

$$E_{t}=E_{P_{e}}+E_{K}=\frac{1}{2}kx^{2}+\frac{1}{2}mv^{2}$$

where x is diplacement and Epe is elastic potential energy. From that you can find mass, and should be able to solve the problem from there.

 

[punjabi_monster]

but you don't have the total energy or the mass, so therefore the equation has two unknowns? right...

 

[Pyrrhus]

This is a conservative system [frictionless surface], so apply the Conservation of Mechanical Energy Law, Remember Mechanical Energy will be the same on any points of this system.

 

[Sirus]

That's basically what I was getting at. I guess I should have been more explicit. Total mechanical energy will be elastic potential energy plus kinetic energy. Follow my instructions from above, but find total mech. energy in terms of the mass (keep that variable). Sorry about my previous error.