Name: Simple Harmonic Motion: Hooke's Law
Uploaded: 2019-07-19
Duration: 17 min 48 s
Description: View this video to learn simple harmonic motion and its associated laws using the oscillation of a spring. Who doesn't love a good oscillation now and again?

Question

Using differential equation of linear S.H.M, obtain the expression for acceleration in S.H.M

Accepted Answer

Simple harmonic motion of an object is defined as a motion where the restoring force is directly proportional to the displacement of the object from its mean position.

The differential equation for S.H.M. is given by

$\frac{d^{2} x}{d t^{2}} + \frac{k}{m} x = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)$

where, $x$ is the displacement of the particle of mass $m$ executing S.H.M. at any instant of time $t$ and $k$ is the force constant.

Let us assume,

$ω^{2} = \frac{k}{m} . . . . . . . . . . . . . . . . . . . . . . . . . (2)$

From equation (1) and equation (2), it can be written that

$\frac{d^{2} x}{d t^{2}} + ω^{2} x = 0 . . . . . . . . . . . . . . . . . . . . . . . (3)$

Hence, the acceleration of the particle is given by

$\begin{array}{rcl} a & = & \frac{d^{2} x}{d t^{2}} \\ = & - ω^{2} x \end{array}$

The negative sign indicates that the displacement and the acceleration of the object acts in the opposite direction.

Using differential equation of linear S.H.M, obtain the expression for acceleration in S.H.M

Important Questions on Oscillations

Learn and Prepare for any exam you want !