Question

If the spring constant of a simple harmonic oscillator is quartered, by what factor will the mass of the system need to change in order for the frequency of the motion to remain the same?mfinal / minitial =

Answer 1

Given

The spring constant of a simple harmonic oscillator is quartered

To find

By what factor will the mass of the system need to change in order for the frequency of the motion to remain the same?

Step-by-step explanation

The frequency of the harmonic oscillator is given by

`\omega=\sqrt{(k)/(m)}`

where k is the spring constant and m is the mass

A/q,

The spring constant is quatered and the frequency remains same.

After the change let the mass be m'

Thus,

`\begin{gathered} \sqrt{(k)/(m)}=\sqrt{((k)/(4))/(m^(\prime))} \\ \Rightarrow m^(\prime)=(m)/(4) \end{gathered}`

Conclusion

The mass should also be quatered so that the fequency is same

`(m^(\prime))/(m)=(1)/(4)`