Question

For the block under SHM shown in the figure, which of the following quantities will increase if the force constant is reduced?

• A. Amplitude
• B. Frequency
• C. Period
• D. Position of block
• E. Total mechanical energy of the block

Answer 1

The correct option is C Period

The equation of motion for block, $ma=-kx$ or $a=-\left(k/m\right)x$

General equation for SHM, $a=-{\omega }^{2}x$

So, angular frequency, ${\omega }^2=k/m$ or $\omega =\sqrt{k/m}$

Also, $\omega =2\pi f$

Thus, frequency, $f=\frac{1}{2\pi }\sqrt{k/m}$

Time period, $T=1/f=2\pi \sqrt{m/k}$

When force constant k is reduced, the time period T will increase.