Oscillations and Waves

Force Law and Energy in Simple Harmonic Motion


  • The rate of change of velocity gives acceleration . The acceleration of the particle in SHM a = − Aw2 sin wt

  where A = Amplitude, w = Angular frequency, t = time.

  • If 'F' is force acting on SHM at a displacement 'Y' from mean position F = −mw2y (w = Angular frequency)
  • Using Newtons second law of motion F = −mw2y and f = −Kx ⇒ \tt w = \sqrt{\frac{K}{M}}
  • The work done to displace simple harmonic oscillator is stored in the form of potential energy U = \frac{1}{2} mw^{2} x^{2} = \frac{1}{2} mw^{2} \sin^{2} wt
  • At mean position KE is maximum and PE is minimum at extreme position KE is minimum and PE is maximum. But total energy is constant.

Force Law of Simple Harmonic Motion View the Topic in this video From 0:19 To 5:36

View the Topic in this video From 0:18 To 12:40

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Both velocity and acceleration of a body executing simple harmonic motion are periodic functions. Velocity amplitude is vmax = ωA and acceleration amplitude is amax = ω2 A.