Question

A large rectangular barge floating on a lake oscillates up and down with a period of 4.5 s. Find the damping constant for the barge, given that its mass is 2.30Ã10^5 kg and that its amplitude of oscillation decreases by a factor of 2.0 in 4.9 minutes.

Answer 1

b = 1084.5 kg/s

Step-by-step explanation:

As we know that the amplitude of damped oscillation is given as

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

here we know that

`A = (A_o)/(2)`

after time t = 4.9 minutes

also we know that

`m = 2.30 * 10^5 kg`

now we will have

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

`(bt)/(2m) = ln2`

`b = (ln2 (2m))/(t)`

`b = (2(ln2)(2.30 * 10^5))/(4.9 * 60)`

`b = 1084.5 kg/s`