The motion of a simple pendulum executing S.H.M. is represented by the following equation.
y = A sin (π t + φ ), where time is measured in second. The length of pendulum is

Solution

Physics sir · 3 steps

Read ω straight off the sine argument, then use ω² = g/L for the length.

1. Read off omega. Compare y = A sin(π t + φ) with y = A sin(ω t + φ). The coefficient of t is the angular frequency, so ω = π rad s⁻¹ and the period is T = 2π/ω = 2 s.
2. Pendulum formula. For a simple pendulum, ω = √(g/L). Square both sides and solve for the length.

   L = g/ω² = 9.81/π² = 9.81/9.87 m ≈ 0.994 m

3. So. The length is about 99.4 cm, which is option (c). This is the familiar seconds pendulum, with a period of 2 s and a length of nearly 1 m.

The idea to keep. The number multiplying t inside the sine is ω in rad/s, not the frequency. For a pendulum, L = g/ω², and a 2 s period always means a length of about 1 m.

Answer from the NTA final answer key. Solution by PrepWiser.