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2015-09-21T16:58:44+05:30

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Angle that the string makes with the vertical line = Ф
                 tan Ф = R / L      ---- (1)
          R = radius of horizontal circle
           L = length of string            m = mass of pendulum bob
         ω =  angular velocity of rotation of bob
 
balancing the forces, as the pendulum is in uniform motion in a circle.  There is no acceleration in vertical direction.  T is the tension i n the string.

   T CosФ = m g      and T sinФ = centripetal force = m R ω²
       =>   tan Ф =  m R ω² / m g
 using (1) we get:   ω² = g / L

 time period = 2 π / ω = 2 π √ (L/g)

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