A vibrating object is wiggling
about a fixed position.
A motion that is regular and
repeating is referred to as
a periodic motion.
Simple Harmonic Motion
– Simple harmonic motion occurs when
the force F acting on an object is
directly proportional to the
displacement x of the object, but in the
– Mathematical statement F = -kx
– The force is called a restoring force
because it always acts on the object to
return it to its equilibrium position.
• Descriptive terms
–The amplitude A is the maximum
displacement from the equilibrium
–The period T is the time for one complete
oscillation. After time T the motion
repeats itself. In general x(t) = x (t + T)
–The frequency f is the number of
oscillations per second. The frequency
equals the reciprocal of the period. f = 1/T.
–Although simple harmonic motion is not
motion in a circle, it is convenient to use
angular frequency by defining ω = 2πf =
Parameter Unit Definition Equation
Time to complete one
Number of cycles per unit
Force that causes the
mass to return to its
equilibrium position F = -kx
Rate of angular
displacement per unit
f = =
T = 2π
Times at Beginning and End of Cycle
1st A to E 0.0 to 2.3 2.3
Mass – Spring Sinusoidal Graph
1. A force of 16 N is required to stretch a
spring a distance of 40 cm from its rest
position. What force (in Newtons) is
required to stretch the same spring …
a. … twice the distance?
b. … three times the distance?
c. … one-half the distance?
Set 1: Simple Pendulum
1. A pendulum makes 35 complete oscillations in 12 s. (a)
What is its period? (b) What is its frequency?
2. (a) A pendulum is 3.500 m long. What is its period at
the North Pole where g = 9.832 m/s2? (b) In Java
3. A pendulum has a frequency of 5.50 Hz on earth at a
point where g = 9.80 m/s2. What would be its frequency
in Jupiter where the acceleration due to gravity is 2.54
times than on earth?
4. A simple pendulum has a period of 2.4 s at a location
where the acceleration due to gravity is 9.7 m/s2. What
is the length of the pendulum?
1. A pendulum extend from the roof of a building
almost to the floor. If the pendulum’s period is
8.5 s, how tall is the buliding?
2. What is the period of a 1.00-m-long pendulum is
a space craft orbiting at 6.70 x 106 m above the
Use the formula: g = G·me/d2 where: me=5.96 x
1024kg, G = 6.67 x01-11N m2/kg2 and d = 6.37 x
2. Perpetually disturbed by the habit of the
backyard squirrels to raid his bird feeders, Mr.
H decides to use a little physics for better living.
His current plot involves equipping his bird
feeder with a spring system that stretches and
oscillates when the mass of a squirrel lands on
the feeder. He wishes to have the highest
amplitude of vibration that is possible. Should
he use a spring with a large spring constant or
a small spring constant?
3. Referring to the previous question. If Mr. H
wishes to have his bird feeder (and attached
squirrel) vibrate with the highest possible
frequency, should he use a spring with a large
spring constant or a small spring constant?