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 S H A K E

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Simple Harmonic Motion

Describe the bobblehead doll’s head.

Periodic FrequencyOscillating PeriodDamping TimePosition SpeedCycle DisplacementMaximum AmplitudeMinimum ForceInterval Equilibrium

Properties of Periodic Motion

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• Definition

– 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 opposite direction.

– 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 position.

– 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 = 2π/T.

The FormulasParameter Unit Definition EquationPeriod (T)

s(Second)

Time to complete one cycle/vibration

1 f

Frequency (f)

Hz(Hertz)

Number of cycles per unit time

1 ω T 2π

Restoring Force (F)

N (newton)

Force that causes the mass to return to its equilibrium position F = -kx

Angular Velocity (ω)

m/s (meter/se

cond)

Rate of angular displacement per unit time

k m

T =

f = =

ω =

T = 2π Lg

Cycle Letters Times at Beginning and End of Cycle (in seconds)

Cycle Time (in seconds)

1st A to E 0.0 to 2.3 2.3

2nd

3rd

4th

5th

6th

Mass – Spring Sinusoidal Graph

Exercise1. 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?

32 N48 N

8 N

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 (g=9.782 m/s2?)

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?

Homework

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 earth’s surface? 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 106 m)

THANK YOU

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?