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Question:

A pendulum is executing simple harmonic motion and its maximum kinetic energy is K1. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K2. Then?

K2=K14

K2=2K1

K2=K12

K2=K1

Solution:

Maximum kinetic energy=1/2mω²A²
ω=√(g/L)
A=Lθ
KE=1/2mgL x L²θ²
KE=1/2mgLθ²
K1=1/2mgLθ²
If length is doubled
K2=1/2mg(2L)θ²
K1/K2 = (1/2mgLθ²)/(1/2mg(2L)θ²) = 1/2
K2=2K1