Simple harmonic motion
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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


  • 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


  • 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


  • For springs:

  • m = mass

  • K = spring constant

  • Mass affects period

    • < mass = < T


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