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Simple harmonic motion

Simple harmonic motion

by Krishnan G -
Number of replies: 1

An ideal pendulum was oscillating with an angular amplitude Θ = ∏/3 inside a stationary elevator. When the pendulum was passing through its equilibrium position, the lift suddenly starts moving upward with an acceleration a = g. Find the new angular amplitude of the oscillation.

a) ∏/3

b) ∏/6

c) cos-13/4

d) ∏/2

Answer is given as option c). Kindly explain.

In reply to Krishnan G

Re: Simple harmonic motion

by Rajat Rao -

Let the initial height be h, final height be H, length of string be L,initial amplitude A, final amplitude B.

By conservation of energy,

mgh=m(g+a)H                   h=2H

L(1-cos(A))=2L(1-cos(B))                  cos(A)=1/2

1-cos(B)=1/4      B=cos-1(3/4)