Name: Simple Harmonic Motion and Harmonic Oscillator
Uploaded: 2019-07-19
Duration: 9 min 10 s
Description: A harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x.

Question

Describe simple harmonic motion as projection of uniform circular motion.

Accepted Answer

Simple harmonic motion is the motion in which the object moves to and fro along a line, under a restoring force that is directed towards mean position.

Consider a particle moving with uniform speed along the circumference of a circle. $X O X'$ and $Y O Y'$ are perpendicular diameters.

This circle is considered as CIRCLE OF REFERENCE with particle $P$ as particle of reference.

As the reference particle moves from $X$ to $Y$ , its projection on diameter $Y O Y'$ moves from $O$ to $Y$ .

As the reference particle moves from $Y$ to $X'$ , its projection on diameter $Y O Y'$ moves from $Y$ to $O$ .

Similarly, as the reference particle moves from $X'$ to $X$ via $Y'$ , its projection on diameter $Y O Y'$ moves from $O$ to $Y'$ and then from $Y'$ to $O$ .

Thus, during the time the particle $P$ completes one revolution, its projection oscillates about the point $O$ along the diameter $Y O Y'$ and completes $1$ vibration.

This motion of projection is a Simple harmonic motion.

Hence, by projecting the uniform circular motion on its diameter gives a simple harmonic motion.

In other words, Simple harmonic motion is projection of uniform circular motion.

Describe simple harmonic motion as projection of uniform circular motion.

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