Question

A harmonic oscillator begins to vibrate with an amplitude of 1.6 m, but after a time of 1.5 minutes, the amplitude has dropped to 0.80 m. What is the time constant of the damping of this oscillator?

Answer 1

Answer:

time constant of the damping 130 seconds

Explanation:

given data

amplitude A1 = 1.6 m

time t = 1.5 min = 90 sec

amplitude A2 = 0.80 m

to find out

time constant of the damping

solution

we know here that maximum amplitude at time t is express as

A2 = A1 × e$e^{\frac{-t}{b} }$       .............a

here b is time constant

so b will be from equation 1

b = $\frac{t}{ln(\frac{A1}{A2} )}$       ............b

put here all value top find b

b = $\frac{90}{ln(\frac{1.6}{0.80} )}$  

b =  $\frac{90}{ln(2)}$

b = 129.84

so time constant of the damping 130 seconds