Pendulums

Concept: Physics (Oscillations) - Displacement Equation for Simple Harmonic Motion (S.H.M.).

Step 1: State the standard displacement equation. For a particle performing S.H.M. released from an extreme position, the angular displacement at time is given by: $ A \omega T T = 2\pi\sqrt{\frac{L}{g}} \omega = \frac{2\pi}{T} \theta A = L\theta A \omega $

Concept: Physics (Oscillations) - Tension in a Simple Pendulum.

Step 1: State the general formula for tension. The tension ( ) in the string at any angle is the sum of the radial component of weight and the required centripetal force: $ \theta = 0 \cos \theta = 1 v_{max} v_{max} = A\omega \omega = \sqrt{\frac{g}{l}} $

Concept: The time period of a simple pendulum is given by the formula where = length of the pendulum, = acceleration due to gravity.

Step 1: Substitute the given values.

Step 2: Simplify the expression.

Step 3: Calculate the time period. Thus, the time period of the pendulum is