Solving Simple Harmonic Motion Problem with Energy

[Glorzifen]

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

E_total = 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]
E_total = 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.

 

[ehild]

[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

 

[dacruick]

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