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SIMPLE HARMONIC MOTION

STARTER

- MAKE A LIST OF OBJECTS THAT EXPERIENCE VIBRATIONS

PERIODIC MOTION

- PERIODIC MOTION Any motion that repeats itself

precisely over equal periods of time. - If that periodic motion is generated by a linear

restoring force it is SIMPLE HARMONIC MOTION.

HOOKEs LAW

- Recall Hookes Law
- F -kx
- x is the amount of extension or compression of a

spring - Spring constant, k , describes the force

necessary to stretch or compress an individual

spring. Each spring is different. - the negative sign indicates that the force always

opposes the direction of the stretch, restoring

the object to its rest or equilibrium position

Quantities that Describe Periodic Motion

- Period the length of time required to complete

one full cycle of motion - Frequency the number of cycles in a given time
- Period and frequency are inversely related

ENERGY

- ET ½ mv2 ½ kx2

- x is the position
- At the ends of the oscillation the mass stops and

changes direction, so all of the energy is

elastic potential energy - At equilibrium (x0) the string is not stretched

so all energy is kinetic.

VELOCITY

- v vmax v 1- x2/A2

- v is the speed of the mass at any position of its

motion - x is any position
- A is maximum amplitude
- vmax is the maximum speed occurs at equilibrium

position

UNIFORM CIRCULAR MOTION

- The amplitude of SHM is equal to the radius of

Uniform Circular Motion - Use the UCM equations to describe SHM
- a 4p2A/T2
- vmax 2pA/ T Or T 2pA/ vmax

PERIOD and FREQUENCY of mass on spring

- Another arrangement for vmax
- vmax2 k/m A2
- Substituting into UCM equation
- T 2pvm/k
- Equation for frequency
- f 1/2p vk/m

PENDULUM

- T 2p v l /g
- l is the length of the pendulum string
- g is acceleration due to gravity
- This equation is valid for the period of a

pendulum for small angles

DEFINITION

- Simple Harmonic Motion a periodic vibratory

motion in which the force is directly

proportional to the displacement