Question

For a damped oscillator with a mass of 300 g, a spring constant 150 N/m and a damping coefficient of 87 g/s, what is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 17 cycles?

Answer 1

`(A)/(A_o) = 0.500`

Step-by-step explanation:

As we know that the Amplitude of Damped oscillation is given by the formula

`A = A_o e^(-bt/2m)`

here we know that

`b = 87 g/s`

m = 300 g

k = 150 N/m

so the time period is given as

`T = 2\pi\sqrt{(m)/(k)}`

now we have

`T = 2\pi\sqrt{(0.300)/(150)}`

`T = 0.28 s`

now total time taken in 17 cycles

`t = 17 T`

`t = 17(0.28) = 4.78 s`

now plug in all values

`A = A_oe^(-87(4.78)/2(300))`

`A = A_o(0.500)`

so we have

`(A)/(A_o) = 0.500`