Simple Pendulum
The vertical distance from the point of suspension and the center of mass of the suspended object, when it is in the mean position, is termed as the length of the simple pendulum, and denoted by L.
A simple pendulum demonstrates periodic motion.
Let the mass of suspended object is ‘m’.
This motion occurs in suspended object (in vertical plane), is mainly due to gravitational force mg.
Calculation of time
Period of simple pendulum
When suspended object is at
point A.
Angle between string with vertical
line passing through the fixed support = θ
Restoring torque on suspended
object= - mgsinθ × L
For small value of angles of
oscillations, sin θ ≈ θ
Restoring torque = -mgLθ
--------- Equation 1
Let I = the
moment of inertia of suspended object = mL2
α = the angular
acceleration = – ω2θ
Restoring torque= I α =
mL2 α --------- Equation 2
=> mL2 α = -mgLθ
=> mL2( – ω2θ) = mgLθ
