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JEE PHYSICS MCQ: OSCILLATIONS

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Application +4 | -1

A particle is making simple harmonic motion along the

X

-axis. If at a distances

{x_1}

and

{x_2}

from the mean position, the velocities of the particle are

{v_1}

and

{v_2}

respectively, then the time period of its oscillation is given as

View answer and explanation

Correct option: D

T = 2\pi \sqrt {\frac{{x_2^2 - x_1^2}}{{v_1^2 - v_2^2}}}

Option D (

T = 2\pi \sqrt {\frac{{x_2^2 - x_1^2}}{{v_1^2 - v_2^2}}}

) is correct because it correctly relates the time period to the given velocities and positions in SHM.

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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)