Simple Harmonic Motion
Simple harmonic motion:
Motion that follows a
repetitive pattern, caused by a
restoring force that is
proportional to displacement
from the equilibrium position.
In the case of this simple
pendulum, what is the restoring
force?
Simple Harmonic Oscillator:
F = - kx
Period of oscillation (T) depends upon
the mass and force constant:
T = 2π
m
k
A small bug (0.30 g) is caught in a spider web and
causes the web to vibrate with a frequency of 15 Hz.
A) What would be the spring constant of this web?
B) If the web trapped a bug that is 1/3 as massive,
what frequency would you predict the web to
vibrate with? Solve quantitatively to assess your
prediction.
A) T = 2π m
k
m = .30 g
f = 15 Hz
k = 4π2m
= 2.7 N/m
2
T
T = 1/f = .067 s
B) 26 Hz
Simple Pendulum: a pendulum in which the mass
is considered to be concentrated in the bob. In
addition, the angle of displacement is relatively
small (less than 15˚)
The period of the pendulum will
be dependent only upon gravity
and the length of the pendulum:
T = 2π
L
g
What must be the length of the simple pendulum in
a grandfather clock that advanced 1.0 s with each
cycle of the pendulum?
L = T2g
2
L
4π
T = 1.0 s
T = 2π
g
= .25 m
How long would it take that same clock to
complete one cycle if it were used on the moon (g
= 1.7 m/s2)?
= 2.4 s
L
T = 2π
= 2π .25 m
g
1.7 m/s2
A 10.0 kg mass stretches a spring 5.00 cm. What
would be the period of oscillation of that spring is
18.0 kg were attached to it and released?
A .50 kg mass at the end of a spring vibrates 3.0
times per second with an amplitude of .15 m. A)
What is the spring constant of the spring? B) What
is the speed of the block when the spring is
compressed .15 m?
A mass causes a spring to oscillate with a frequency
of .88 Hz. When .600 kg is added to the spring, its
frequency is .60 Hz. What was the original mass?
You want to make pendulum clock so that a single
swing one time across will advance the clock one
second. How long should you make the pendulum?
What is the period of a simple pendulum that is
.250 m long. What would be the period be in an
orbiting space shuttle?
What is the frequency of a simple pendulum with a
2.00 kg bob and a length of .650 m?
A simple pendulum on earth has a period of 1.00 s
on earth. What is the period of that pendulum on
the moon where g = 1.67 m/s2?
A pendulum on earth has a period of .00670 s on
the surface of the earth. Aboard a launching rocket
ship, its period changes to .00310 s. What is the
acceleration of the launching rocket ship?
A pendulum of length 2.50 m is used near the
“surface” of Saturn and completes 4.00 full cycles
in 11.8 s. What must be the acceleration due to
gravity on Saturn?
A pendulum used on earth is timed for 6.0 s. If the
length of the pendulum was measured as .994 m,
how many cycles did it complete?