Chapter 12Vibrations and Waves

Periodic MotionAny repeated motion

Examples?

a

b

c

Describe velocity, force and acceleration at a, b and c

c is the equilibrium or rest positionThe force is called the restoring force

Any periodic motion where the restoring force is proportional to the

displacement is called simple harmonic motion

Frestore = -kx

Hooke’s Law

Felastic = -kx

spring force

- because force is opposite displacement

spring constant: how stiff the spring is

x = displacement from rest position

I have a mass of 85 kg. I jump on a trampoline and it compresses 40 cm before propelling me up. What is the spring constant of the trampoline?

Felastic = Fweight

Fweight = mg

Fweight = 834 N

x = 0.40 m

k = -F/-x = 2085 N/m

A pendulum moves in simple harmonic motion when displacement angles are

small, less than 15°

FT

mg

Fgy

Fgx

FT

Net Force?acceleration?velocity?

Forces on a Pendulum

mg

Net Force?acceleration?velocity?

Time MeasurementsPeriod, T, is the time for one back and forth motion in secondsFrequency, f, is how often back and forth motions occur in 1 second, measured in hertz, Hz

sec11 Hz

Tf 1

Period of a Pendulum

gLT 2

Period only depends on L, the length of the pendulum

Period of a mass-spring system

kmT 2