Question

The motion of a simple pendulum executing S.H.M. is represented by the following equation.

y = Asin(πt + Φ), where time is measured in seconds. The length of the pendulum is ______.

Options

• 97.23 cm

• 25.3 cm

• 99.4 cm

• 406.1 cm

Answer 1

The motion of a simple pendulum executing S.H.M. is represented by the following equation.

y = Asin(πt + Φ), where time is measured in seconds. The length of the pendulum is 99.4 cm.

Explanation:

During the time period of SHM,

`T = 2pisqrt(l/g)` and, `omega = (2pi)/T`

Hence, `omega = (2pi)/(2pi)sqrt(g/l)`

`omega = sqrt(g/l)`

`l = g/omega^2`

By comparing with the above equation, we get;

ω = π

Hence, `l = g/(pi^2) ≈ 99.4` cm