Question

A simple pendulum of length 1 m has a mass of 10 g and oscillates freely with
amplitude of 2 cm, the potential energy at the extreme point is:

Answer 1

time period of simple pendulum is given by, T = 2π√{l/g}

we also know, angular velocity ($\omega$) is given by, $\omega=\frac{2\pi}{T}$

or, $T=\frac{2\pi}{\omega}$

so, time period can be changed into angular velocity , $\omega=\sqrt{\frac{g}{l}}$

given, g = 10m/s² , l = 1m

so, $\omega=\sqrt{10}$ rad/s

know, potential energy at extreme position, U = $\frac{1}{2}m\omega^2A^2$

given, m = 10g = 10^-2 kg, A = 2cm = 2 × 10^-2

so, U = 1/2 × 10^-2 × (√10)² × (2 × 10^-2)²

= 1/2 × 10^-2 × 10 × 4 × 10^-4 J

= 20 × 10^-6 J

= 2 × 10^-5 J

hence, answer is 2 × 10^-5 J