E-1
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
8.02
Spring 2005
Review E: Simple Harmonic Motion and Mechanical Energy
This Worked Example demonstrates the basics of
Simple Harmonic Motion (SHO)
and
so is included as a review unit.
An object of mass
2
4.0
10
kg
m
−
=
×
sitting on a frictionless surface is attached to one end
of a spring. The other end of the spring is attached to a wall. Assume that the object is
constrained to move horizontally along one dimension. The spring has spring
constant
2
2.0
10 N/ m
k
=
×
. The spring is initially stretched a distance
2.0cm
from the
equilibrium position and released at rest.
a)
What is the position of the mass as a function of time?
b)
What is the velocity of the mass as a function of time?
c)
What is the time that it takes the mass-spring system to first return to its original
configuration?
d)
How do the initial conditions for the position and velocity of the mass-spring
system enter into the solution?
e)
What is the kinetic energy of the mass as a function of time?
f)
What is the potential energy of the spring-mass system as a function of time?
g)
What is mechanical energy of the spring-mass system as a function of time?
Solutions:
a) Choose the origin at the equilibrium position. Choose the positive
x
-direction to the
right. Define
( )
x t
to be the position of the mass with respect to the equilibrium position.

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