Question

A ball is attached to an ideal spring and oscillates with a period t. if the mass of the ball is doubled, what is the new period?

Answer 1

The new timeperiod is 1.41 times the old time period.


Now, consider a mass, m with time period "t" is oscillating.

Then,
The time period of a the oscillation of the ball is given as 2π
`\sqrt{ (m)/(k) }`

Now, if we need to find the time period,'t' when mass is doubled i.e 2m
`image`'=
`\frac{2 \pi \sqrt{ (m)/(k) } }{2 \pi \sqrt{ (2m)/(k) } }`

or, t' = t
`√(2)` = 1.41 t