—
1
—
Problem.
Simple harmonic oscillator
In this problem you will use one of the most important conservation laws in Physics,
conservation
of energy
to calculate the period of a simple harmonic oscillator. The ﬁgure below displays a mass
m
, which is attached to a spring with a spring constant
k
.
x
unstretched
stretched
m
m
k
k
At
t
= 0
, the spring is stretched to a distance
A
from the unstretched state and released from
rest. We then let is oscillate indeﬁnitely (assuming there is no friction involved), and measure the
displacement
x
(
t
)
from the unstretched state as a function of time.We will ﬁnd the period of this
oscillatory system by solving a differential equation relating the displacement
x
(
t
)
to its derivative,
i.e., the velocity of the mass
m
.
a) Finding the
initial conditions
: ﬁnd the value of the position,
x
(
t
)
, and velocity,
dx/dt
, of
the mass
m
at the time
t
= 0
.
b) Finding the
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 '07
 BERMAN
 Calculus, Conservation Of Energy, Energy, Kinetic Energy, Potential Energy, Simple Harmonic Oscillator

Click to edit the document details