91Ó°ÊÓ

SHM stands for Simple Harmonic Motion. It can be defined as the motion in which an object moves back and forth along a line.

Time for one oscillation is same as period of oscillation. Mathematically it is given by,

$T=2\mathrm{Ï€}\sqrt{\frac{m}{k}}.......\left(1\right)$

Here, $T$is the period of oscillation in seconds

$M$is the mass of object in kilograms

$k$is the spring constant of spring $\left(N/m\right)$

The force of an object moving in x-direction is given by,

$F=m{a}_x.....\left(2\right)$

But in case of SHM, the force due to spring having soring constant is given by,

$F=-kx.......\left(3\right)$

From equation. (2) and (3).

$\begin{array}{l}m{a}_x=-kx\\ .·.\frac{m}{k}=-\frac{x}{a_x}\end{array}$

Substitute above expression in equation. (1)

$T=2\mathrm{Ï€}\sqrt{-\frac{x}{a_x}}$

The expression for period of oscillation was derived as

$T=2\mathrm{Ï€}\sqrt{-\frac{x}{a_x}}$

Substitute values in above expression to get the time for one oscillation

$$\begin{gathered} T=2\mathrm{Ï€}\sqrt{-\left(\frac{0.3m}{-1.80m/s^2}\right)} \\ =2\mathrm{Ï€}\sqrt{\frac{0.3m}{1.80m/s^2}} \\ =2.57s \end{gathered}$$

Therefore, the time for one oscillation is 2.57 s .