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Simple Harmonic Motion. Back & forth & back & forth Are you getting sleepy?. Harmonic motion – back & forth over the same path. X = displacement – distance pulled/stretched from equilibrium When released – spring exerts a force on the mass towards equilibrium V max @ equilibrium

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simple harmonic motion

Simple Harmonic Motion

Back & forth & back & forth

Are you getting sleepy?

harmonic motion back forth over the same path
Harmonic motion – back & forth over the same path
  • X = displacement – distance pulled/stretched from equilibrium
  • When released – spring exerts a force on the mass towards equilibrium
  • Vmax @ equilibrium
  • p causes it to overshoot
  • @ max stretch/compression –
    • V = 0, acceleration & force @ max
remember hooke s law
Remember Hooke’s Law?
  • Felastic = -kx

Pendulums

pendulum
Pendulum
  • Disregard mass of string, air resistance, friction
  • If restoring F proportional to displacement = harmonic motion
  • Small angles of displacement equal simple harmonic motion
  • Free body diagrams (miss them?!) to

Resolve into x & y components

slide5

Amplitude = max displacement from equilibrium (rad or m)

    • Angle of pendulum, spring stretched/compressed
  • Period = one full cycle of motion (T) in seconds
    • Time per cycle
    • Depends on length of the string & free fall acceleration
  • Frequency = # of cycles through a unit of time (f) in Hertz

or

slide6

L = length of the string

  • g = acceleration due to gravity
  • String length varies = different arc lengths to travel through = different T
  • Mass varies = no effect on T (more force to restore equilibrium but more force to start)
  • Amplitude = affected by g
slide7

For springs:

  • m = mass
  • K = spring constant
  • Mass affects period
    • < mass = < T
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