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Simple Harmonic Motion And Uniform Circular Motion - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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  • Simple harmonic as projection of circular motion is considered one of the most asked concept.

  • 9 Questions around this concept.

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Two particles are performing simple harmonic motion in a straight line about the same equilibrium point.  The amplitude and time period for both particles are same and equal to A and T, respectively.  At time t = 0 one particle has displacement A while the other one has displacement  \frac{-A}{2}    and they are moving towards each other.  If they cross each other at time t, then t is :

 

For particle \mathrm{P} revolving round the centre \mathrm{O} with radius of circular path \mathrm{r} and angular velocity , as shown in below figure, the projection of \mathrm{OP} on the \mathrm{x}-axis at time \mathrm{t} is

Concepts Covered - 1

Simple harmonic as projection of circular motion

Simple harmonic can be represented as a projection of circular motion.

If P moves uniformly on a circle as shown in the below figure, then its projection P′ on a diameter of the circle executes SHM.

As the particle P moves on the circle, The position of P′ on the x-axis is given by

x(t) = A cos (ωt + φ)

This is the equation of SHM on the x-axis with amplitude A and angular frequency as \omega

Where A is the radius of the circle

and \phi  is the angle that the radius OP makes with the x-axis at t=0

Similarly, The position of P′ on the y-axis is given by

y(t)=  A sin (ωt + φ)

This also an SHM of the same amplitude as that of the projection on the x-axis, but differing by a phase of π/2.

 

 

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Simple harmonic as projection of circular motion

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Simple harmonic as projection of circular motion

Physics Part II Textbook for Class XI

Page No. : 347

Line : 1

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