1118 Simple Harmonic Motion

1
11/18 Simple Harmonic Motion

• HW Simple Harmonic Motion Due Thursday 11/21
• Exam 4 Thursday 12/5 Simple Harmonic Motion
  Angular Acceleration and TorqueAngular
  MomentumIm out of town Monday 12/2 (after
  Thanksgiving)

2
Simple Harmonic Motion (SHM)

• Real objects are elastic (to some extent)
• Elastic
• Object returns to original shape after
  deformation
• Original shape called Equilibrium
• Object resists deformation with force
• Force called Restoring Force
• Force proportional to deformation
• Force is in opposite direction to
  deformationForce points toward equilibrium,
  deformation points away from equilibrium

3
Simple Harmonic Motion (SHM)

• Definitions
• Displacement ?x ? deformation from equilibrium
• Equilibrium ? Fnet 0 as usual
• Oscillation ? one complete cycle
• Period T ? time for one complete oscillation
• Frequency f ? of oscillations in one second
  example 1.65Hz (in units of Hertz)
• Amplitude A ? maximum displacement from
  equilibrium

4
Hookes Law Simple Harmonic Motion
Force always points toward the equilibrium
position.
FSpring -k ?x
?x is displacement (compression or extension)
from equilibrium.
Simple harmonic motion only when the force is
proportional to the displacement, ?x, as in
Hookes law.
5
k
m
motion is symmetric, max displacement left max
displacement right
6
k
m
Warning!!!! The acceleration is not constant so
a ? ?v/?t !!! vave ? mid-time velocity!!! Fnet
does equal ma, however
motion is symmetric, max displacement up max
displacement down
7
(No Transcript)
8
What we find
9
A block hangs from a spring and is pulled down 10
cm and released. It bounces up and down at a
rate of 3 times every second. How could this
rate be increased?

• You may choose any of
• increase the mass
• decrease the mass
• push it faster
• make the spring stiffer
• make the spring less stiff
• pull it down farther
• dont pull it down as far
• other?

10
What matters?

• Period (or frequency) affected by
• spring constant (k)
• mass (m)
• amplitude (A)
• initial conditions
• (how we get it going)

Yes
Yes