Question

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\(\sqrt \frac{1}{g}\). Think of a qualitative argument to appreciate this result

Answer 1

Restoring force that brings body of pendulum back to its mean position 

F = – mg sinθ 

Form small θ, sinθ ≈ θ = v/T

If approximation for sinθ = θ is not taken into account then Time period T >2π \(\sqrt \frac {1}{g}\) This happens when θ is not small.