Question

Two balls of unequal mass are hung from two springs that are not identical. The springs stretch the same distance as the two systems reach equilibrium. Then both springs are compressed and released. Which one oscillates faster?

a) The spring with the heavier ball,
b) Springs oscillate with the same frequency,
c) The spring with the light ball.

Answer 1

b) Springs oscillate with the same frequency,

Step-by-step explanation:

expression for frequency of vibration of mass hanging from a spring is given as follows

f =
`(1)/(2\pi) * \sqrt{(k)/(m) }`

k is force constant of spring and m is mass vibrating .

In the present case, if mass stretches the spring by x and remains balanced

mg = k x

`(k)/(m) =(g)/(x)`

g and x are same for both cases

`(k)/(m)` will also be same for both cases .

Hence frequency of vibration will also be same for both the balls .