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Philosophy
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An oscillatory motion is in general governed by a differential equation which looks like

 

d2y/dt2 + a1dy/dt + a2y = M(t)

 

where y(t) : is a parameter whose time evolution is studied: displacement of a pendulum, current or charge in a circuit etc. a1 and a2 are positive constants, where a1 could be zero or non zero. M(t) could be zero or non-zero periodic quantity, like a periodic driving force.

 

  •  Simple Harmonic motion (Pendulum -> LC circuit) 

      d2y/dt2 + a2y = 0

 

  •  Damped simple Harmonic motion (Pendulum – LCR       circuit)

 d2y/dt2 + a1dy/dt + a2y = 0

 

  •        Forced damped simple Harmonic motion (Resonance in an LCR circuit) 

         d2y/dt2 + a1dy/dt + a2y = F0 Sin(ωt)

 

 

  •      Coupled Harmonic oscillators (Two LC circuits coupled with a capacitor)

     

 

  • Nonlinear harmonic oscillators (Pendulum) 

d2y/dt2 + a2f(y) = 0

 

 

 

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