A pendulum of length L = 1 m is released from an initial angle of 15° . After 1000 s, its amplitude is reduced to 2.5º. What is the value of the time constant, T?

Question

asked Feb 9, 2020 53.2k views

1 Answer

Tetsuya · Answer 1 · 2020-02-16T02:48:34+0000

Answer:

The value of the time constant is 558.11 sec.

Step-by-step explanation:

Given that,

Pendulum length = 1 m

Initial angle = 15°

Time = 1000 s

Reduced amplitude = 2.5°

We need to calculate the value of the time constant

Using formula of damping oscillation

$\theta=\theta_(0)e^{(t)/(\tau)}$

Where,
$\theta$ =amplitude

$\theta_(0)$ =amplitude at t = 0

Put the value into the formula

$2.5=15e^{(-1000)/(\tau)}$

$(1)/(6)=e^{(-1000)/(\tau)}$

$ln(1)/(6)=(-1000)/(\tau)$

$\tau=(1000)/(-ln(1)/(6))$

$\tau=558.11\ sec$

Hence, The value of the time constant is 558.11 sec.