# Solving Simple Harmonic Motion Problem with Energy

## Homework Statement

A 500g block on a spring is pulled 20cm and released. The motion has a period 0.8s.

What is the velocity when the block is 15.4cm from the equilibrium?

## Homework Equations

Etotal = 0.5kx2 + 0.5mv2
w = $$\sqrt{k/m}$$
w = 2pi*f
f = 1/T

## The Attempt at a Solution

[FINDING K]
f = 1/0.8 = 1.25
w = 2pi*(1.25) = 7.85
7.85 = $$\sqrt{k/0.5}$$
k = 30.8

[FINDING TOTAL ENERGY BY USING THE INITIAL VALUES]
Etotal = 0.5(30.8)(0.2)2
= 0.616

[USING THE TOTAL ENERGY WITH THE SECOND SET OF VALUES TO FIND V]
0.616 = 0.5(30.8)(0.154)2 + 0.5(0.5)(v)2
x = 1.7

Make sense to me...just hope its right. Any comments? Thanks as always - I appreciate the effort.

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ehild
Homework Helper

[USING THE TOTAL ENERGY WITH THE SECOND SET OF VALUES TO FIND V]
0.616 = 0.5(30.8)(0.154)2 + 0.5(0.5)(v)2
x = 1.7

It is all right, up to the last line. What is x? and what is 1.7? And how much is v?

ehild

yeah its all good except you missed some calculations. My answer is around 1 I think.