A simple pendulum of length 1 m is inside a vehicle accelerating horizontally at 7.5 m/s². Take g = 10 m/s². If the square of the angular frequency about the new equilibrium is N/4 s⁻², find N.
Physics · Simple Harmonic Motion · angular shm and its time period
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Question

A simple pendulum of length 1 m is inside a vehicle accelerating horizontally at 7.5 m/s². Take g = 10 m/s². If the square of the angular frequency about the new equilibrium is N/4 s⁻², find N.

G1 Physics · Accepted Answer

Effective gravity is gₑ = √(g²+a²) = √(10²+7.5²) = √(100+56.25) = 12.5 m/s². For small oscillations, ω² = gₑ/l = 12.5/1 = 25/2. Write 25/2 = 50/4. Hence, N = 50.