Question

A weightless spring which has a force constant $k$ oscillates with frequency $f$ when a mass $m$ is suspended from it. The spring is cut into two halves and a mass $2m$ is suspended from one of the halves. The frequency of oscillation will now be

• A. $f$
• B. $2f$
• C. $f/2^{1/2}$
• D. $f\times 2^{1/2}$

Answer 1

The correct option is C $f/2^{1/2}$

The frequency f of the oscillator is the number of complete vibrations per unit time and is given by-

$f=1/2k/m$

We know, $f_1=1/2\pi k/m\to 1$

also, $f_2=1/2\pi \sqrt{2}k/m\to 2$

Dividing $2$ by $1$

$f_2/f_1=\left(1/2\pi \sqrt{2}\right)\left(1/2\pi k/m\right)$

$=\sqrt{2}$

So, $f_2=\sqrt{2}{f}_1\to 3$