Physics Course/Oscillation/Oscillation Side by Side

      Oscillation Side by Side

      When apply a force on an object of mass attach to a spring . The spring will move a distance y above and below the equilibrium point and this movement keeps on repeating itself for a period of time . The movement up and down of spring for a period of time is called Oscillation

      1

      The force acts on the object to pull the object down

      F = m a

      The Restoring Force of spring to push the object up can be calculated by Hook's Law

      Fs = - k y

      The oscillation stops when the two forces are equal or the net force on object is zero

      m a = - k y
      y = \frac{m a}{k}
      a = - \frac{k}{m} y
      t = \frac{k}{m} \frac{y}{v}

      2

      Any force acting on an object can be expressed in a differantial equation

      F = m \frac{d^2y}{dt^2}

      Equilibrium is reached when F = Fs

      F = m \frac{d^2y}{dt^2} = - k y
      F = \frac{d^2y}{dt^2} + \frac{k}{m} y = 0
      s^2 + \frac{k}{m} s = 0
      s = ± j \sqrt{\frac{k}{m}}
      s = e^ j\sqrt{\frac{k}{m}}t + e^ -j\sqrt{\frac{k}{m}}t
      y = A Sin {\frac{k}{m}}t
      Last modified on 3 March 2011, at 18:57