What is a simple pendulum ? Show that motion executed by the bob of a pendulum is SHM. Derive an expression for it's time period. What is meant by second's pendulum ?
Answers
Explanation:
The Simple Pendulum
A practical simple pendulum is a small heavy sphere(bob) suspended by a light and inextensible string from a rigid support. The length of the simple pendulum is the distance between the point of suspension and centre of gravity of heavy sphere.
The Simple Harmonic Motion Pendulum
The motion of Simple Pendulum as Simple Harmonic Motion
When we pull a simple pendulum from its equilibrium position and then release it, it swings in a vertical plane under the influence of gravity. It begins to oscillate about its mean position. Therefore, the motion is periodic and oscillatory. Now, if we displace the pendulum by a very small angle Θ, then it performs the simple harmonic motion.
Simple Pendulum
Consider a simple pendulum having mass ‘m’, length L and displaced by a small angle Θ with the vertical. Thus, it oscillates about its mean position. In the displaced position, two forces are acting on the bob,
Gravitational force, which is the weight of the bob – ‘mg’ acting in the downward direction.
Tension T’ in the string.
Now, weight mg is resolved in two components,
Radial component mgcosΘ along the string.
Tangential component mgsinΘ perpendicular to the string.