# 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.

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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.