1. Tardigrade
  2. Question
  3. Physics
  4. 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?

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Q. 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?

Oscillations

Solution:

We know that, for a spring mass system, restoring
force, $F _{s}=-k x$ (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.