Lecture 3: Period, Phase, Amplitude and Energy of SHM


Readings: Textbook , Chapter 13.5

Equations of SHM

x = A cos(ω t + φ0)
v = - A ω sin(ω t + φ0)
a = -A ω2 cos(ω t + φ0)
ω = ( k/m )1/2
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Energy in SHM

We consider physical Harmonic Oscillator - mass m moving under the action of restoring force Fx = - k x . One can think spring and Hooke's law, but this is a general setup for Harmonic Oscillator

  • Physical system has energy, E . It is the sum of the kinetic and potential energy
    E=K+U = ½ m vx2 + ½ k x2
  • Compute E in SHM
    E = ½ m A2ω2 sin2(φ) + ½ k A2 cos2(φ) = ½ k A2 [sin2(φ)+cos2(φ)]
  • Total energy of SHM is conserved !
    E = ½ k A2 = constant
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