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JEE PHYSICS MCQ: OSCILLATIONS

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A particle is subjected to two mutually perpendicular simple harmonic motions such that its

x

and

y

coordinates are given by

x=2 \sin \omega t,\,y=2 \sin \left(\omega t+\frac{\pi}{4}\right)

The path of the particle will be

View answer and explanation

Correct option: A

An ellipse

Option A is correct because the equations for x and y describe an ellipse due to the phase difference between the two SHMs.

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Assertion: A particle executing simple harmonic motion comes to rest at the extreme positions.

Reason: The resultant force on the particle is zero at these positions. A particle is subjected simultaneously to two SHM’s one along the

x

-axis and the other along the

y

-axis. The two vibrations are in phase and have unequal amplitudes. The particle will execute A particle is executing SHM with amplitude

a

. When the PE of a particle is one-fourth of its maximum value during the oscillation, its displacement from the equilibrium position will be The displacement, velocity and acceleration in a simple harmonic motion are related as the Assertion: Angular velocity of earth around sun is lesser than the angular velocity of moon about earth.
Reason: Time taken by moon revolve around earth is less than time taken by earth to revolve around sun. A particle is executing

SHM

. At a displacement

{y_1}

its potential energy is

{U_1}

and at a displacement

{y_2}

its potential energy is

{U_2}

. The potential energy of the particle at displacement

\left( {{y_1} + {y_2}} \right)