Question

Which of the following Expressions Does not represent SHM:
$(A)A\cos \omega t$
$(B)A\sin 2\omega t$
$(C)A\sin \omega t + B\cos \omega t$
$(D)A{e^{\sin \omega t}}$

Answer 1

A very common type of periodic motion is called the Simple harmonic motion. A system that Oscillates with simple harmonic motion is called the simple harmonic Oscillator.
In SHM the net force is proportional to the displacement and acts in the opposite direction of the displacement.
In SHM The direction of the restoring force is always towards the mean position.

Complete step-by-step solution:
The simple harmonic motion is given by,
$\;a\left( t \right){\text{ }} = {\text{ }} - {\omega ^{2\;}}x\left( t \right)$
Here, $\omega$ is the angular Velocity of the Particle.
Simple harmonic motion can be expressed as an oscillatory motion, here the acceleration of the particle at any position is directly proportional to the displacement from the mean position. It is also referred to as the special case of oscillatory motion.
All the Simple Harmonic Motions are said to be oscillatory and also periodic but not all the oscillatory motions are SHM.
The Simple Harmonic Motion is the most useful tool for understanding the characteristics of sound waves, light waves, and alternating currents.
It is a special case of oscillation with a straight line between the two extreme points. The path of the SHM is Constraint.
Here, Option (D) is the correct answer.

Note: $A{e^{\sin \omega t}}$ it doesn’t represent Simple harmonic motion
The SHM can serve as the Mathematical model for various motions. The motion of the undamped pendulum approximates the simple Harmonic motion if the angle of oscillation is small. The force responsible for the SHM is always towards the equilibrium position and directly proportional to the distance from it.