1
OBJECTIVE
a)
Calculate the acceleration of gravity ‘g’ and compare with expected value by
analyzing the motion of a pendulum moving with Simple Harmonic
Motion(SHM).
b)
Calculate the length of a pendulum so that it can be used a pendulum clock.
EQUIPMENT
1.
2m length of string
2.
1 large support rod, 1 small support rod, and 1 clamp
3.
hanger
4.
stopwatch
5.
2m stick
THEORY
Consider a pendulum of length ‘L’ and mass ‘m’.
Suppose the pendulum is swinging and
at an instant in time its angular position is ‘
θ
’ with respect to the vertical.
The FreeBody
diagram for the pendulum is shown below at this instant in time.
1.
Show that by applying N2L in the tangential direction (
Σ
F
t
= ma
t
) and by assuming
small oscillations (small
θ
), the following equation must be satisfied:
2
2
0
dg
dt
L
θ
+=
Simple Harmonic Equation
THE SIMPLE PENDULUM (Simple Harmonic Motion)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
2.
Confirm that the solution to this equation is given by:
()
cos
(
)
m
tt
θ
θω
φ
=+
Solution to SHM Equation
Where,
θ
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 Luna
 Acceleration, Gravity, Simple Harmonic Motion, Periodic function, Simple Harmonic, SHM Equation

Click to edit the document details