JEE PHYSICS MCQ: OSCILLATIONS

1 Medium

1 of 1

Analyzing +4 | -1

The velocity of a particle moving in the

x-y

plane is given by:

\frac{d x}{d t}=8 \pi \sin 2 \pi t

and

\frac{d y}{d t}=5 \pi \cos 2 \pi t

where,

t=0

, the path of the particle is

View answer and explanation

Correct option: B

An ellipse

The path of the particle is an ellipse (Option B) because the x and y coordinates satisfy the equation of an ellipse after integration and elimination of the time variable.

More Questions from OSCILLATIONS

Practice All Chapter MCQs →

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)