Solving Simple Harmonic Motion Problem with Energy

AI Thread Summary
The discussion focuses on solving a simple harmonic motion problem involving a 500g block on a spring. The user calculates the spring constant (k) as 30.8 and the total energy (Etotal) as 0.616 using initial conditions. They attempt to find the velocity of the block when it is 15.4cm from equilibrium by applying energy conservation principles. However, there is confusion regarding the final calculations, particularly the meaning of "x" and the value of "v." Another participant suggests that the final velocity should be around 1, indicating that the initial calculations may have errors.
Glorzifen
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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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Glorzifen said:


[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.
 

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