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

Answer:

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$e^{-\frac{t}{2\tau}}$        

Now, putting the value in the above relation:

x(t) = 1.8$e^{-\frac{75}{2\times 32}}$

x(t) = 1.8$e^{-1.17}$

x(t) = 0.558 m