Question

A damped oscillator has an initial amplitude of 1.8 m and a time constant of 32 s. What is its amplitude after 75 s?

Answer 1

The amplitude after 75 s, x(t) = 0.558 m

Given:

Initial Amplitude, A = 1.8 m

time constant,
`\tau` = 32 s

Solution:

Now, to calculate the amplitude of the damped oscillation after 75 s, we use the relation:

Amplitude after 75 s, x(t) = A
`e^{-(t)/(2\tau)}`

Now, putting the value in the above relation:

x(t) = 1.8
`e^{-(75)/(2* 32)}`

x(t) = 1.8
`e^(-1.17)`

x(t) = 0.558 m