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

time constant of the damping 130 seconds

Step-by-step 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^{(-t)/(b) }` .............a

here b is time constant

so b will be from equation 1

b =
`(t)/(ln((A1)/(A2) ))` ............b

put here all value top find b

b =
`(90)/(ln((1.6)/(0.80) ))`

b =
`(90)/(ln(2))`

b = 129.84

so time constant of the damping 130 seconds