Question

I. Time period of a spring-mass system depends on its amplitude.
II. Time period of a spring-mass system depends on its mass.
III. Time period of a spring-mass system depends on spring constant.
Which of the following statement(s) is/are correct?

• A. Both I and II
• B. Both I and III
• C. Both II and III
• D. I, II and III

Answer 1

Answer: (C)

We know that, for a spring mass system, restoring
force, $F_s=-kx$ (spring force)
where, $k$ is spring constant.
$F=-m{\omega }^{2}x\text{ (for SHM condition) }$
On comparing Eqs. (i) and (ii), we get
$\omega =\sqrt{\frac{k}{m}}$
$\Rightarrow T=2\pi \sqrt{\frac{m}{k}}\left(\because T=\frac{2\pi }{\omega }\right)$
$\Rightarrow T\propto \sqrt{m}$
$\Rightarrow T\propto \frac{1}{\sqrt{k}}$
So, time period $T$ does not depends on the amplitude of the oscillation
but depend on $m$ and $k$.
So, statements II and III are correct but I is incorrect.