Lab 10: Simple Harmonic Motion, Pendulum
Only 3 more to go!!
2
A
Mass's Displacement
length = l

T
T
T
C
A
B
0
C
B
-mgcos
-2
0
2
4
6
8
Time
mg
mg
-mgsin
mg
The x-component of the weight is the force that is restoring the mass to equilibrium!
This is analogous to F = -kx from last week’s lab.
10
It turns out we can write the displacement as a function of time, t (same as last
week):
x = xMAX cos(t)
The velocity can be written as: V = -  xMAX sin(t),
The acceleration: a = - 2 xMAX cos(t)
Remember that,  is the angular frequency, and it tells us how
many oscillations occur per second.
For a pendulum system:

g
l
where g, is the acceleration
of gravity and l, is the length
of the pendulum
Another useful quantity is the period, T. The period tells us how long it takes
to complete one oscillation, for a pendulum system:
2
l
T
 2

g
What are we doing today? 2 experiments.
The first will allow us to finally answer the questions? “Does size matter….for a
pendulum?”
The second experiment we will increase the length of the pendulum and measure the
period. Then we will plot T2 vs L
12
10
2
8
2
2
Period (sec )
Slope = 4 /g
6
4
2
1
2
3
4
Length (meters)
5
6