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

Disclaimer: Compete.etutor.co may from time to time provide links to third party Internet sites under their respective fair use policy and it may from time to time provide materials from such third parties on this website. These third party sites and any third party materials are provided for viewers convenience and for non-commercial educational purpose only. Compete does not operate or control in any respect any information, products or services available on these third party sites. Compete.etutor.co makes no representations whatsoever concerning the content of these sites and the fact that compete.etutor.co has provided a link to such sites is NOT an endorsement, authorization, sponsorship, or affiliation by compete.etutor.co with respect to such sites, its services, the products displayed, its owners, or its providers.

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.