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$\sqrt{ \frac{m}{k} }$

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

or, t' = t$\sqrt{2}$ = 1.41 t