Q14PE - College Physics (Urone)

Question

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?

Step-by-Step Solution

Answer

The mass is need to be changed by a factor of 2.

Step 1: Expression for the frequency of SHM

The frequency of simple harmonic motion depends on the mass and the force constant. The expression is as follows,

 

\({\bf{f = }}\frac{{\bf{1}}}{{{\bf{2\pi }}}}\sqrt {\frac{{\bf{k}}}{{\bf{m}}}} \)

 

Here, m is the mass and k is the force constant.

Step 2: Determination of the factor by which mass is to be changed

It can be observed from the expression of the frequency that frequency is directly proportional to \(\sqrt {\frac{k}{m}} \) which means that same factor of the value of mass and force constant will cancel out. So, for maintaining the value of frequency when the value of k is doubled, the value of m need to be change by the factor of 2.

 

Thus, the mass is need to be changed by a factor of 2.