Question

14. If the spring constant of a simple harmonic oscillator is doubled, by what factor will the mass of the system need to change in order for the frequency of the motion to remain the same?

Answer 1

Lets se

And

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

`\\ \rm\Rrightarrow √(k)T=2\pi√(m)`

So

`\\ \rm\Rrightarrow k\propto m`

If spring constant is doubled mass must be doubled