What causes the restoring force in a simple pendulum?

Question

What causes the restoring force in a simple pendulum?

A. friction between the thread and the support

B. the force exerted on the pendulum bob while displacing it from the mean position

C. the component of the weight of the bob acting perpendicular to the thread

D. the component of the weight of the bob acting parallel to the thread

Answer 1

C

The equation of motion is, using F = ma,



-mgsinA = mLd^A/dt^2 where A is the angle the string makes with the downward vertical, L is the length of the string, m is the mass and d^2A/dt^2 is the angular acceleration.



If A is small then sinA ~ A so we get



-mgsinA = mLd^A/dt^2 ~ -mgA where A is in radians



i.e. d^A/dt^2 ~ - (g/L) A which is roughly SHM with time period T = 2pi[sqrt(L/g)] for a simple pendulum...

Answer 2

....is due to gravity, and the preserved gravitational potential energy inside the pendulum. When the pendulum goes up on any side, its height relative to the equilibrium state increases, so this increase in height causes a potential energy to be preserved in the pendulum. the force acting on pendulum is always the same, but the component of this force that is tangent to the pendulum's trajectory, increases, so the acceleration of the pendulum toward the center (equilibrium state) increases, so the pendulum's velocity lowers, it stops, reverses direction and starts accelerating toward the center.

Answer 3

C. the component of the weight of the bob acting perpendicular to the thread