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Simple Harmonic Motion

Simple Harmonic Motion. Masses & Springs 2.03. Simple harmonic motion (SHM) occurs when the acceleration and the displacement are related by: a = -Cx where C is a constant. Mass/Spring System. F = -kx ( Hooke’s Law) But F = ma so a = (-k/m)x SHM. The Displacement for SHM.

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Simple Harmonic Motion

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  1. Simple Harmonic Motion Masses & Springs 2.03 Simple harmonic motion (SHM) occurs when the acceleration and the displacement are related by: a = -Cx where C is a constant.

  2. Mass/Spring System F = -kx ( Hooke’s Law) But F = ma so a = (-k/m)x SHM

  3. The Displacement for SHM

  4. Example A mass on a spring ( m = .100kg ) has a displacement given by: Find: The spring constant k The period of the motion. 1. 8.10 N/m 2. 2.21 seconds

  5. The Pendulum

  6. Pendulum Example A student wants to make a pendulum with a mass and a string that has a period of 1.00 second. How long should the string be? = .248m = 24.8cm

  7. Energy in SHM Mass/Spring System: KE = (1/2)mv2 PE = (1/2)kx2 E total = (1/2)kx2max = KE + PE v = 0 : PE = E = (1/2)kx2max x = 0 : KE = E = (1/2)kx2max

  8. Example A .500kg mass on a spring ( k = 400N/m ) is pulled back .25m and released from rest. Find: The maximum velocity. The total energy. The maximum force on the mass. The period of the motion. 1.= 7.07 m/s 2. E = (1/2)kx2max= (1/2)(400)(.252 )= 12.5J 3. Fmax = kxmax = 400(.25) = 100N = .222 seconds

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