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?

Please show all of your steps.

Answer 1

Let's look at hookes law

$\\ \rm\rightarrowtail F=-kx$

Apply Newton's second law

$\\ \rm\rightarrowtail ma=-kx$

$\\ \rm\rightarrowtail m\propto k$

So if spring constant is doubled mass will be doubled also