Simple Harmonic Motion

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Periodic Motion

Motion reoccurs in a regular pattern Simple harmonic motion (SHM): force that

restores the object to equilibrium is directly proportional to the displacement

Two important measurements: Period (T): time to repeat one complete cycle Amplitude: maximum displacement

Mass on a Spring

Hooke's Law: force exerted by a spring is directly proportional to the amount the spring is stretched

F = -kx PE=(1/2)kx2

http://web.hep.uiuc.edu/home/mats/WCIA/wcia_030430_1.wmv

Springs!

Masses & Springs 2.02

Example

A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from the end. What is the spring constant?

Known: x=0.18m F=56N F=-kx so k=F/x (the negative just means it's a

restoring force) k=56N/0.18m = 310 N/m

Example Continued

How much PE is stored in the spring? PE=(1/2)kx2

PE=(1/2)(310N/m)(0.18m)2

PE=5 J

Now you try it!

A 560 N bicyclist sits on a bicycle seat and compresses the two springs that hold it up. The spring constant is 2.2 x 104 N/m for each spring. How much is each spring compressed?

Know: F=560 N k=2.2 x 104 N/m 2 springs F=-kx or x=F/k and since 2 springs x=F/2k X=1.3 x 10-2 m

Period of a Spring

Mass attached to a spring exhibits simple harmonic motion

T= 2π√(m/k) Frequency is inverse of

period!

Pendulum

Object (bob) suspended by a string of length l String exerts tension (force) and gravity exerts

force Period of a pendulum: T=2π√(l/g)

Sample Problem

A pendulum with length 36.9 cm has a period of 1.22 s. What is the acceleration of gravity at the pendulum's location?

Known: T=1.22 s l=0.369 m T=2π√l/g so g=(2π)2l

(T)2

g=9.78 m/s2