1. Simple Harmonic Motion

Solutions of Differential Equations of SHM

The differential equation for the Simple harmonic motion has the following solutions:

  • x=Asinωt (This solution when the particle is in its mean position point (O) in figure (a)
  • x0​=Asinϕ (When the particle is at the position & (not at mean position) in figure (b)
  • x=Asin(ωt+ϕ) (When the particle at Q at in figure (b) (any time t).

These solutions can be verified by substituting this x values in the above differential equation for the linear simple harmonic motion.

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