SHM in short

  • Simple harmonic motion is simplest form of oscillatory motion
  • SHM is a kind of motion in which the restoring force is propotional to the displacement from the mean position and opposes its increase.Mathematically restoring force is
    F=-Kx
    K=Force constant
    x=displacement of the system from its mean or equilibrium position
    Diffrential Equation of SHM is
    d2x/dt2 + ω2x=0

     
  • Solutions of this equation can both be sine or cosine functions .We conveniently choose
    x=Acos(ωt+φ)
    where A,ω and φ all are constants
  • Quantity A is known as amplitude of SHM which is the magnitude of maximum value of displacement on either sides from the equilibrium position
  • Time period (T) of SHM the time during which oscillation repeats itself i.e, repeats its one cycle of motion and it is given by
    T=2π/ω
    where ω is the angular frequency
  • Frequency of the SHM is the number of the complete oscillation per unit time i.e, frequency is reciprocal of the time period
    f=1/T
    Thus angular frequncy
    ω=2πf
  • Total energy remains constant in a SHM.So you can find the energy at any position and differentiate it to find the out the frequency
  • Problem of SHM are basically to find out the timeperiod.So the concenteration should be on getting the net restoring force
  • The basic approach to solve such problem is
    1. Consider the system is displaced from equilibrium position
    2. Now consider all the forces acting on the system in displaced position
    3. find the restore force which comes out to be in the form
    4.F=-kx

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