Transcript Simple Harmonic Motion

Vibrations and Waves
Simple Harmonic Motion
Hooke’s Law

Periodic motion – repeated motion


Usually back and forth over the same path at regular
time intervals
Equilibrium position – the point in the motion where
the net force on an object is zero

At the equilibrium point, velocity reaches a
maximum
 At maximum displacement. Spring force and
acceleration reach a maximum

Velocity is zero
Hooke’s Law
Hooke’s Law
harmonic motion – vibration about
an equilibrium position in which a restoring
force is proportional to the displacement
from equilibrium
 Hooke’s Law = spring force = -(spring
constant * displacement)
 Felastic = -kx
 k is measured in N/m
 Felastic is measured in N
 Simple
Hooke’s Law
 Remember
that stretched or compressed
objects have elastic potential energy

This causes the object to repeat its motion
The Simple Pendulum

A simple pendulum consists of a bob and string



The bob – the part of the pendulum that swings back
and forth
We disregard the mass of the string, air resistance,
and friction
The restoring force of a pendulum is a
component of the bob’s weight
 The same conclusions that we drew with springs
about force, displacement, and velocity are true
for pendula as well, with small angles
The Simple Pendulum
The Simple Pendulum
 At
the equilibrium point, velocity reaches a
maximum
 At maximum displacement, force and
acceleration reach a maximum

Velocity is zero
 Gravitational
potential energy increases as
a pendulum’s displacement increases

Kinetic energy increases as the pendulum
nears the equilibrium point
The Simple Pendulum
The Simple Pendulum