Write the laws of simple pendulum.

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A simple pendulum of length $L$ is constructed from a point object of mass $m$ suspended by a massless string attached to a fixed pivot point. $A$ small peg is placed a distance $2L/3$ directly below the fixed pivot point so that the pendulum would swing as shown in the figure below. The mass is displaced $5$ degrees from the vertical and released. How long does it take to return to its starting position?

Time period of a simple pendulum in a stationary lift is ' $T$ '. If the lift accelerates with $\frac{ g }{6}$ vertically upwards then the time period will be .....

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  • [JEE MAIN 2022]

A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than $90^o$. At its highest point, the string is cut. Which trajectory is possible for the bob afterwards.