Question
Answer the following:
(b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than 2π √l/g
Think of a qualitative argument to appreciate this result.
Solution
In the case of a simple pendulum, the restoring force acting on the bob of the pendulum is given as,
F = –mg sinθ where,
F = Restoring force
m = Mass of the bob
g = Acceleration due to gravity
θ = Angle of displacement
For small θ, sinθ ≈ θ
For large θ, sinθ is greater than θ.
Hence, the time period increases as:
T =
