Find the period of small oscillations of a simple pendulum of length λ if its point of suspension has constant acceleration a⃗ = α₁ î - α₂ ĵ with respect to Earth.
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Question

Find the period of small oscillations of a simple pendulum of length λ if its point of suspension has constant acceleration a⃗ = α₁ î - α₂ ĵ with respect to Earth.

G1 Physics · Accepted Answer

In the accelerating frame, effective gravity is g′=|g⃗-a⃗ of frame|. With a⃗=α₁î-α₂ĵ and upward ĵ, the components are -α₁ horizontally and -(g-α₂) vertically. Thus g′=√[(g-α₂)²+α₁²]. Therefore T=2π√[l/g′]. Correct option: 1.