genmoum

1. Genevieve Moum
53480142
Energy in Simple Harmonic Motion
The two mass-spring systems on the left
have the same equilibrium position, x=0. In
system a, the spring is being stretch to a
position of x=X. In system c, the spring is
being compressed to length x=-X. Which
system currently has more work stored as
elastic potential energy?
Solution
Elastic Potential Energy is equivalent to (1/2)kA2 where A is the distance the mass is
from the equilibrium position. If we plug in our distances in both mass-spring systems,
we get (1/2)kX2 (for system a) and (1/2)k(-X)2=(1/2)kX2 (for system b). These are
equivalent. Thus if the absolute value of the distance from the equilibrium position is
the same, then both systems will have the same elastic potential energy.
Conceptually, this makes sense as well. When a spring is stretched, it wants to get
back to its equilibrium position; this is why post-release it immediately bounds away
from the hand. The same can be said when a spring is compressed; it wishes to move
back to the equilibrium position, and thus upon release it moves in that direction.
Because in either system the distance from the equilibrium position is the same, the
spring has to oscillate it’s way back to the equilibrium position through the same
distance. Therefore, the elastic potential energies must be the equivalent.