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.

HOOKE’s LAW Recall Hooke’s 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 E T = ½ mv 2 + ½ kx 2 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 (x=0) the string is not stretched so all energy is kinetic.

VELOCITY v = v max √ 1- x 2 /A 2 v is the speed of the mass at any position of its motion x is any position A is maximum amplitude v max 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 = 4π 2 A/T 2 v max = 2πA/ TOr T = 2πA/ v max

PERIOD and FREQUENCY of mass on spring Another arrangement for v max v max 2 = k/m A 2 Substituting into UCM equation T = 2π√m/k Equation for frequency f = 1/2π √k/m

PENDULUM T =2π √ 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