Question

A mass on a spring oscillates with a period T. Part A If both the mass and the force constant of the spring are doubled, the new period will be If both the mass and the force constant of the spring are doubled, the new period will be a. 4T. b. 2√T. c. T. d. T2√. e. T4.

Answer 1

The new time period will be T.

Step-by-step explanation:

The time period in terms of spring constant and mass is given by :

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

If mass and force constant is doubled, m' = 2m and k' = 2k

New time period is given by :

`T'=2\pi\sqrt{(m')/(k')}`

`T'=2\pi\sqrt{(2m)/(2k)}`

`T'=2\pi\sqrt{(m)/(k)}`

`T'=T`

So, the new period will remains the same. Hence, the correct option is (C).