EASY

Earn 100

Explain reference circle of simple harmonic motion.

Important Questions on Oscillations

MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

In case of a simple harmonic motion, if the velocity is plotted along the $X$ -axis and the displacement (from the equilibrium position) is plotted along the $Y$ -axis, the resultant curve happens to be an ellipse with the ratio:
$\frac{major axis (along X)}{minor axis (along Y)} = 20 π$

What is the frequency of the simple harmonic motion?

HARD

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A particle is performing a linear simple harmonic motion of amplitude

A

. When it is midway between its mean and extreme position, the magnitudes of its velocity and acceleration are equal. What is the periodic time of the motion?

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A particle performs

S . H . M .

with amplitude

A

. Its speed is tripled at the instant when it is at a distance of

\frac{2 A}{3}

from the mean position. The new amplitude of the motion is

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A particle executing S.H.M. has velocities

v_{1}

and

v_{2}

at distance

x_{1}

and

x_{2}

respectively from mean position. The angular velocity

(ω)

of the particle is given by

HARD

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A particle performs linear SHM. At a particular instant, the velocity of the particle is

u

and acceleration is

α

(both having the same direction). At another instant velocity is

v

and acceleration is

β (0 < α < β)

(both in opposite direction to each other).The distance between the two positions is

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A particle executes S.H.M., the graph of velocity as a function of displacement is :

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A simple pendulum oscillates harmonically about

x = 0

with an amplitude

A

and time period

T

. Its speed at

x = A / 2

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A body of mass

10 g

is executing simple harmonic motion about a point with an amplitude

20 cm .

If its maximum velocity is

100 cm \cdot s^{- 1},

its velocity will be

50 cm . s^{- 1}

at a distance of

cm

from its mean position.

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is

MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A particle performs simple harmonic motion with amplitude A. Its speed is tripled at the instant that it is at a distance

\frac{2 A}{3}

from equilibrium position. The new amplitude of the motion is:

MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A body undergoing simple harmonic motion has a maximum acceleration of

8 m s^{- 2}

and maximum speed of

1.6 m s^{- 1} .

What is the time period

T ?

HARD

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A particle executes simple harmonic motion with an amplitude of

5 cm

. When the particle is at

4 cm

from the mean position, the magnitude of its velocity in

SI

units is equal to that of its acceleration. Then, its periodic time in seconds is:

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A particle is oscillating according to the equation

V (t) = 4 \sin 0.4 π t

metres. In how much time after the motion begins will that particle reach the extreme position from the mean position?

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A particle executes S.H.M. with amplitude

A

and time period

T

. The displacement of the particle when its speed is half of maximum speed is

\frac{\sqrt{x} A}{2} .

The value of

x

MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

The velocity of a body while passing through the mean position is

10 m s^{- 1}

. What will be the frequency of it, if it is executing SHM of amplitude

1 m

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A simple harmonic motion has amplitude

a

and time period

T

. The maximum velocity will be

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A simple pendulum performing harmonic motion has an amplitude $A$ and period $T .$ The speed of the bob at $x = \frac{A}{2}$ is

MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

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:

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A particle is executing SHM along a straight line. Its velocities at distances

x_{1}

and

x_{2}

from the mean position are

V_{1}

and

V_{2}

respectively. Its time period is:

MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion as a Projection of Uniform Circular Motion

A mass is suspended from a vertical spring which is executing S.H.M. of frequency

5 Hz

. The spring is unstretched at the highest point of oscillation. The maximum speed of the mass is [acceleration due to gravity

g = 10 m s^{- 2}

]

Explain reference circle of simple harmonic motion.

Important Questions on Oscillations

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