A simple pendulum consists of a light string tied at one end to a pivot point and attached to a mass at the other end. The period of a pendulum is the time it takes.
Simple Pendulum - Definition, Time period, Derivation, Total Energy What is Simple Pendulum?A point mass attached to a light inextensible string and suspended from fixed support is called a simple pendulum. The vertical line passing through the fixed support is the mean position of a simple pendulum.The vertical distance between the point of suspension and the centre of mass of the suspended body (when it is in mean position) is called the length of the simple pendulum denoted by L. Table of Content:.Overview:A simple pendulum is a mechanical arrangement that demonstrates periodic motion. Time Period of Physical PendulumConsider a body of irregular shape and mass (m) is free to oscillate in a vertical plane about a horizontal axis passing through a point, weight mg acts downward at the centre of gravity (G).⇒ Check:If the body displaced through a small angle (θ) and released from this position, a is exerted by the weight of the body to restore to its equilibrium.τ = -mg × (d sinθ)τ = I ατ α = – mgdsinθI = d 2θ/dt 2 = – mgdsinθWhere I = moment of inertia of a body about the axis of rotation.d 2θ/dt 2 = (mgd/I) θ Since, sinθ ≈ θω 0 = √mgd/I. Time Period of Physical PendulumT = 2π/ω 0 = 2π × √I/mgdFor ‘I’, applying,I = I cm + md 2Therefore, the time period of a physical pendulum is given by,T = 2π × √(I cm + md 2)/mgd⇒ Also Read:.
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.A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth.
The mathematics of are in general quite complicated. Simplifying assumptions can be made, which in the case of a allow the equations of motion to be solved analytically for small-angle oscillations.