- #1
Tanya Sharma
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Homework Statement
A simple pendulum of length l is tied to the ceiling of an elevator which is at rest. The pendulum is oscillating with a time period T, and it has an angular amplitude β. Now at some time when the bob of the pendulum is at the mean position, the elevator suddenly starts moving down with acceleration a. What is the new angular amplitude of the pendulum?
Homework Equations
The Attempt at a Solution
I tried a few things but haven’t been able to come with something useful.
When the elevator is at rest the governing equation is ##\frac{d^2θ}{dt^2} = -\frac{g}{L}θ ## .
When the elevator accelerates down the governing equation is ##\frac{d^2θ}{dt^2} = -\frac{(g-a)}{L}θ ##.
This doesn't help much .
When thinking about energy conservation , I think energy is not conserved between the times when the elevator is at rest and when it accelerates down.
I would be grateful if somebody could help me with the problem .