# SHM - Energy Equation

1. Jan 19, 2014

### Oneablegal

1. The problem statement, all variables and given/known data

A 7kg weight is affixed to a spring with a constant of 327 N/m. System undergoing SHM.
Position x is -1.22m and velocity of positive 3.54 m/s. The system then moves to a position where the velocity is positive 4.73. Find the position where the velocity is 4.73 m/s

2. Relevant equations

I know that velocity increases in a + direction to the left of equilibrium. The initial position I am given,-1.22m is to the left of the equilibrium point, and I know the weight is speeding up toward the equilibrium point. I believe the relevant equation here is the conservation of mechanical energy for a mass-spring system.

3. The attempt at a solution

1/2mvf^2 + 1/2kxf^2 = 1/2mvi^2 + 1/2kxi^2
The 1/2 cancels

And I am stuck on how to set up the equation. I know if mvf^2 = kxi^2, then vf = √(kxi^2)/m, but that is for velocity, where is a known... ugh! I need a bump in the right direction so I can do this myself. I need to find Xf, and I think I need to take a negative square root somewhere... The book solution tells me the answer is -1.13m, but I am working on trying to figure out how To get there.

Please kick me in the right direction, so I can solve and understand this problem. Thank you!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 19, 2014

### voko

So you have $$m v_f^2 + k x_f^2 = m v_i^2 + k x_i^2 .$$ Of all the symbols in the equation, you know $k, \ m, \ v_i, \ v_f, \ x_i$. The only unknown is $x_f$. Solve for it.

3. Jan 19, 2014

### Oneablegal

Ah! Thank you! It was looking me right in the face! Got it!

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