A simple pendulum of length $l = 0.5 m$ is hanging from ceiling of a car. The car is kept on
a horizontal plane. The car starts accelerating on the horizontal road with acceleration of
$5 m / s^{2}$ . Find the time period of oscillations of the pendulum for small amplitudes
about the mean position.

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Solution

Pseudo acceleration $5 ㎨$ acts on the pendulum in the opposite direction of car motion. Effective acceleration on pendulum is $g^{'} = \sqrt{5^{2} + 10^{2}} = 5 \sqrt{5} ㎨$
Time period of pendulum $T = 2 π \sqrt{\frac{l}{g}} = 2 π \sqrt{\frac{0.5}{5 \sqrt{5}}} = 4.21 s e c$

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A simple pendulum of length l=0.5m is hanging from ceiling of a car. The car is kept on a horizontal plane. The car starts accelerating on the horizontal road with acceleration of 5m/s2. Find the time period of oscillations of the pendulum for small amplitudes about the mean position.

Pseudo acceleration 5㎨ acts on the pendulum in the opposite direction of car motion. Effective acceleration on pendulum is g′=√52+102=5√5㎨Time period of pendulum T=2π√lg=2π√0.55√5=4.21sec

A simple pendulum of length $l = 0.5 m$ is hanging from ceiling of a car. The car is kept on
a horizontal plane. The car starts accelerating on the horizontal road with acceleration of
$5 m / s^{2}$ . Find the time period of oscillations of the pendulum for small amplitudes
about the mean position.

Pseudo acceleration $5 ㎨$ acts on the pendulum in the opposite direction of car motion. Effective acceleration on pendulum is $g^{'} = \sqrt{5^{2} + 10^{2}} = 5 \sqrt{5} ㎨$
Time period of pendulum $T = 2 π \sqrt{\frac{l}{g}} = 2 π \sqrt{\frac{0.5}{5 \sqrt{5}}} = 4.21 s e c$