MEDIUM

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What is extreme position in SHM?

Important Questions on Oscillations

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

A body is in simple harmonic motion with time period

T = 0.5 s

and amplitude

A = 1 cm

. Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.

MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

A simple pendulum is attached to a block which slides without friction down an inclined plane $(A B C)$ having an angle of inclination $α$ as shown while the block is sliding down the pendulum oscillates in such a way that at its mean position the direction of the string is,

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MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

A particle moves according to the law,

x = r c o s \frac{π t}{2}

. The distance covered by it the time interval between

t = 0 t o t = 3 s

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

If the differential equation for a simple harmonic motion is

\frac{d^{2} y}{d t^{2}} + 2 y = 0

, the time period of the motion is,

MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

A light balloon filled with helium of density,

ρ_{H e}

is tied to a long light string of length,

l

and the string is attached to the ground. If the balloon is displaced slightly in the horizontal direction from the equilibrium and released then.

HARD

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

A load of mass $m$ falls from a height $h$ on the scale pan hung from a spring as shown. If the spring constant is $k$ and the mass of the scale pan is zero and the mass $m$ does not bounce relative to the pan, then the amplitude of vibration is

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HARD

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

A simple pendulum of length $l$ is made to oscillate with amplitude of $45$ degrees. The acceleration due to gravity is $g$ . Let $T_{0} = 2 π \sqrt{\frac{l}{g}} .$ The time period of oscillation of this pendulum will be

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

Which of the following equation represents a simple harmonic motion? (

ω

is angular frequency, A is amplitude of oscillation and

i = \sqrt{- 1}

)

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

A particle is performing SHM starting from extreme position. Graphical representation shows that, between displacement and acceleration, there is a phase difference of

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

A particle of mass

m

is moving along the

x - a x i s

under the potential

V (x) = \frac{k x^{2}}{2} + \frac{λ}{x^{'}}

where

k

and

x^{'}

are positive constants of appropriate dimensions. The particle is slightly displaced from its equilibrium position. The particle oscillates with the angular frequency

(ω)

given by

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

x, v

and

a

denote the displacement, the velocity and the acceleration of a particle executing

S H M

of time period

T

. Then, which of the following does not change with time?

HARD

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

A particle moves with simple harmonic motion in a straight line. In first

τ s

, after starting from rest it travels a distance a, and in next

τ s

it travels 2a, in same direction, then :

MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

A particle executes simple harmonic motion between

x = - A

and

x = + A

. If it takes a time

T_{1}

g_{0}

from

x = 0

x = A / 2

and

T_{2}

to go from

x = A / 2

x = A

. Then

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the figure.
Question Image

y

-projection of the radius vector of rotating particle

P

MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

A simple harmonic oscillator of frequency

1 Hz

has a phase of

1

radian. By how much should the origin be shifted in time so as to make the phase of the oscillator vanish. (time in seconds).

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

The weight suspended from a spring oscillates up and down. The acceleration of weight will be zero at

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

A particle of mass

0.1 kg

is executing simple harmonic motion of amplitude

0.1 m

. When the particle passes through the mean position, its kinetic energy is

8 \times 10^{- 3} J

. If the initial phase is

45 °,

the equation of its motion is (Assume,

x (t)

as the position of the particle at time

t

)

MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

Many random snapshots using a camera are taken of a particle in simple harmonic motion between,

x = - x_{0}

and

x = + x_{0}

with origin

x = 0

as the mean position. A histogram of the total number of times the particle is recorded about a given position (event no) would most closely resemble,

EASY

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

Which of the following plots represents schematically the dependence of the time period of a pendulum if measured and plotted as a function of its oscillations? (Note: amplitude need not be small)

MEDIUM

Physics>Oscillations and Waves>Oscillations>Simple Harmonic Motion

The position co-ordinates of a particle moving in a $3 D$ coordinate system is given by

$x = a \cos ω t$

$y = a \sin ω t$

and $z = a ω t$

The speed of the particle is:

What is extreme position in SHM?

Important Questions on Oscillations

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