Match List ‐ I (Event) with List ‐ II (Order of the time interval for the happening of the event) and select the correct option from the options given below the lists. List-I List-II ( a ) The rotation period of earth ( i ) 10 5 s ( b ) Revolution period of earth ( ii ) 10 7 s ( c ) Period of a light wave ( iii ) 10 - 15 s ( d ) Period of a sound wave ( iv ) 10 - 3 s

( a ) ‐ ( i ) , ( b ) ‐ ( ii ) , ( c ) ‐ ( iii ) , ( d ) ‐ ( iv )

( a ) ‐ ( ii ) , ( b ) ‐ ( i ) , ( c ) ‐ ( iii ) , ( d ) ‐ ( iv )

( a ) ‐ ( i ) , ( b ) ‐ ( ii ) , ( c ) ‐ ( iv ) , ( d ) ‐ ( iii )

( a ) ‐ ( ii ) , ( b ) ‐ ( i ) , ( c ) ‐ ( iv ) , d ‐ ( iii )

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A person is listening to a tone of 500 Hz sitting at a distance of 450 m from the source of the sound. What is the time interval between successive compressions from the source?

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Important Questions on Oscillations

HARD

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

A particle executes simple harmonic motion and it is located at

x = a, b

and

c

at time

t_{0}, 2 t_{0} a n d 3 t_{0}

respectively. The frequency of the oscillation is:

HARD

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

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>Periodic and Oscillatory Motions

A particle performs simple harmonic motion with a period of

2

second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is

\frac{1}{a} s .

The value of

a

to the nearest integer is

HARD

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is

10 s^{- 1} .

At,

t = 0

the displacement is

5 m .

What is the maximum acceleration? The initial phase is

\frac{π}{4}

HARD

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

Match List $‐ I$ (Event) with List $‐ II$ (Order of the time interval for the happening of the event) and select the correct option from the options given below the lists.

	List-I		List-II
$(a)$	The rotation period of earth	$(i)$	$10^{5} s$
$(b)$	Revolution period of earth	$(ii)$	$10^{7} s$
$(c)$	Period of a light wave	$(iii)$	$10^{- 15} s$
$(d)$	Period of a sound wave	$(iv)$	$10^{- 3} s$

HARD

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

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>Periodic and Oscillatory Motions

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance

\frac{R}{2}

from the earth's centre, where

R

is the radius of the earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period:

MEDIUM

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

The displacement time graph of a particle executing SHM is given in figure: (sketch is schematic and not to scale)

Question Image

Which of the following statements is/are true for this motion?

(A) The force is zero at $t = \frac{3 T}{4}$
(B) The magnitude of acceleration is maximum at $t = T$
(C) The speed is maximum at $t = \frac{T}{4}$
(D) The $P . E .$ is equal to $K . E .$ of the oscillation at $t = \frac{T}{2}$

MEDIUM

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

Frequency of oscillation of a body is

5 Hz

when a force

F_{1}

is applied and

12 Hz

when another force

F_{2}

is applied. If both forces

F_{1}

and

F_{2}

are applied together, then frequency of oscillation of the body will be

MEDIUM

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

The function

(\sin ω t - \cos ω t)

represents the S.H.M having a time period

T

MEDIUM

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

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:

EASY

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

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>Periodic and Oscillatory Motions

In an engine the piston undergoes vertical simple harmonic motion with amplitude 7cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to :

HARD

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

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:

HARD

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

A piston is performing

S . H . M .

in the vertical direction with a frequency of

0.5 Hz

. A block of

10 kg

is placed on the piston. The maximum amplitude of the system such that the block remains in contact with the piston is

MEDIUM

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

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).

MEDIUM

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

HARD

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies

ω_{1}

and

ω_{2}

and have total energies

E_{1}

and

E_{2}

, respectively. The variations of their momenta

p

with positions

x

are shown in the figures. If

\frac{a}{b} = n^{2}

and

\frac{a}{R} = n

, then the correct equation(s) is (are)

Question Image

EASY

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

The oscillation of a body on a smooth horizontal surface is represented by the equation,

X = A \cos (ω t)

, where

X =

displacement at time

t

ω =

frequency of oscillation,

a =

acceleration at time

t

and

T =

time period.
Which one of the following graph shows correctly the variation

a

with

t

HARD

Physics>Oscillations and Waves>Oscillations>Periodic and Oscillatory Motions

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$ . The piston and the cylinder have equal cross-sectional area $A$ . When the piston is in equilibrium, the volume of the gas is $V_{0}$ and its pressure is $M_{0}$ . The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[Assume the system is in space.]

A person is listening to a tone of 500 Hz sitting at a distance of 450 m from the source of the sound. What is the time interval between successive compressions from the source?

Important Questions on Oscillations

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