Question:

A simple pendulum performs simple harmonic motion about x=0 with an amplitude 'a' and time period 'T'. The speed of the pendulum at x=a/2 will be:

πaT

3π2aT

πa√3T

πa√3/2T

As simple pendulum performs simple harmonic motion.
∴velocity, v = ω√a² - x²
At, x = a/2
v = (2π/T)√a² - (a/2)² = (2π/T)√3a²/2 = πa√3/T