Sections 13.113.3

1
Simple Harmonic Motion

• Chapter 13
• Sections 13.1?13.3
• Christian Ellenbecker

2
Oscillation

• Periodic Motion repeats itself in a definite
  cycle, it has a stable equilibrium and a
  restoring force that acts upon displacement from
  equilibrium
• Frequency 1/T or w SQRT(k/m) force const./mass
• Restoring force is schizophrenic(return to
  equil.)
• NOT constant
• The net restoring force is directly proportional
  to the displacement? Fx -kx (Hookes Law)
• This is Simple Harmonic Motion (SHM)
• Examples are Springs and Pendula
• SHM conditions true only for small displacements

3
SHM Conditions

• Amplitude does not effect the frequency, and its
  the smoothest function you can do.
• Displacement, velocity and acceleration are
  sinusoidal functions of time
• Cos we hate him, hes a big, fat, lazy, bastard
• A sin2? f t0, remember 2?f w
• Phase just means that we didnt start our clocks
  at the same time
• Amp and Phase are determined by initial state.

4
Energy

• Conserved in SHM and can be expressed in terms of
  the force constant k and the amplitude A
• E1/2(mvx2)1/2(kx2)1/2(kA2)
• This energy is constant, as the body oscillates
  the energy continually transforms back and forth
  from potential to kinetic energy

5
Equation Nominations

• x(t) Asin2?f t?
• a(t) -w2Asinwt ? -w2x(t)
• E1/2(mvx2)1/2(kx2)1/2(kA2)
• Thank You