A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration a. Then the time period is given by T=2π√ℓ/g, where g is equal to

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(4) √g²+a². Idea: work in the trolley's frame, where the bob feels gravity plus a pseudo-force. Weight: mg vertically downward. Pseudo-force: ma horizontally, opposite to the trolley's acceleration. The two are perpendicular, so the resultant has magnitude m√g²+a². The bob hangs along that resultant, and it plays the part of gravity for the swing. g_eff=√g²+a²

A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration a. Then the time period is given by T=2π√ℓ/g, where g is equal to

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