How does the time period of a simple pendulum vary in accelerated frames than in inertial frames?

Question

Does the time period of a simple pendulum increase, decrease or remain the same if it is hanged from the ceiling of an accelerated car, or an elevator..?

Answer 1

The period of a pendulum consisting of a point mass for a bob is given by

T = 2*pi*sqrt (L / a)

where
L is the distance from the point of suspension to the center of mass of the bob, and
a is the acceleration acting on the bob.

If the pendulum is in an inertial frame of reference near the earth's surface, the value of a is g, the acceleration of gravity. If the pendulum is suspended from a point that is accelerating upward, this will effectively add to the effect of gravity, shortening the pendulum's period. Similarly, if the pendulum is accelerating downward, the acceleration subtracts from gravity, lengthening the period. If the suspension point and the pendulum are in freefall, the pendulum won't operate at all because there will effectively be no restoring force to restore the bob to its equilibrium position.

Answer 2

sin A = 0.34m/one million.sixty 5 m => A = 11.89 deg the place A= attitude string made with vertical permit T be tension in string, T cos A = mg ---(one million) T sin A = ma -- (2) (2) / (one million) tan A = a /g a = 9.80 one * tan 11.89 = 2.07 m/s answer m = mass of pendulum