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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. 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

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  1. Simple Harmonic Motion Back & forth & back & forth Are you getting sleepy?

  2. 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

  3. Remember Hooke’s Law? • Felastic = -kx Pendulums

  4. 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

  5. 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

  6. 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

  7. For springs: • m = mass • K = spring constant • Mass affects period • < mass = < T

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