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 )

COLUMN A COLUMN B 1. Periodic motion (a) Sewage disposal system 2. Light (b) Ground water stored between the layers of hard rock 3. Polar animals (c) Rotation of the earth on its own axis 4. Septic tank (d) Travels in a straight line 5. Aquifer (e) Strong sense of smell

1. Periodic motion is the one that occurs at regular intervals of time. The rotation of the earth is similar to periodic motion. 2. Light travels in a straight line until it hits something else. This property of light is known as rectilinear propagation of light. 3. Polar animals have a strong sense of smell so that they can find food that is hidden in the snow. This property they used to find seal breathing holes in the ice. 4. Septic tanks are used to contain domestic sewage from where it flows for basic treatment. The septic tank is a buried, water-tight container usually made of concrete, fibre glass, or polyethylene. 5. An aquifer is an underground water-bearing system consisting of layers of hard rock and other unconsolidated materials. COLUMN A COLUMN B 1. Periodic motion (c) Rotation of the earth on its own axis 2. Light (d) Travels in a straight line 3. Polar animals (e) Strong sense of smell 4. Septic tank (a) Sewage disposal system 5. Aquifer (b) Ground water stored between the layers of hard rock

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The restoring force of a system of mass executing SHM is $4 N$ . If its displacement is $4 cm$ then the force constant is

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Important Questions on Oscillations

HARD

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

The metallic bob of simple pendulum has the relative density

5

. The time period of this pendulum is

10 s

. If the metallic bob is immersed in water, then the new time period becomes

5 \sqrt{x} s

. The value of

x

will be _____ .

MEDIUM

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

A simple pendulum suspended from the ceiling of a stationary lift has a time period $T_{0}$ . When the lift descends at uniform speed, the time period is $T_{1}$ . When the lift descends with constant acceleration, the time period is $T_{2}$ . Which of the following is correct?

HARD

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

The potential energy of a particle of mass

4 kg

in motion along the

x

-axis is given by

U = 4 (1 - \cos 4 x) J

. The time period of the particle for small oscillation

(\sin θ ≃ θ)

(\frac{π}{K}) s

. The value of

K

is _____ .

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.]

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

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

The displacement of simple harmonic oscillator after

3

seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is

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

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

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:

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	$(iv)$	$10^{- 3} s$

MEDIUM

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

Identify the function which represents a periodic motion

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:

EASY

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

Does this displacement-time graph represent periodic motion? What is the period of motion (in case of periodic motion)?
Question Image

HARD

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

COLUMN A	COLUMN B
1. Periodic motion	(a) Sewage disposal system
2. Light	(b) Ground water stored between the layers of hard rock
3. Polar animals	(c) Rotation of the earth on its own axis
4. Septic tank	(d) Travels in a straight line
5. Aquifer	(e) Strong sense of smell

EASY

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

Does this represent periodic motion: A freely suspended bar magnet displaced from its N-S direction and released.

EASY

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

Does this displacement-time graph represent periodic motion? What is the period of motion (in case of periodic motion)?
Question Image

MEDIUM

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

Two masses

m_{1} and m_{2}

suspended together by a massless spring of spring constant K. When the masses are in equilibrium,

m_{1}

is removed without disturbing the system. The angular frequency of

m_{2}

EASY

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

A particle is undergoing simple harmonic motion. The graph shows variation of velocity of particle with its position from mean position. The frequency of simple harmonic motion is,

Question Image

EASY

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

Does this represent periodic motion: A hydrogen molecule rotating about its centre of mass.

The restoring force of a system of mass executing SHM is 4 N. If its displacement is 4 cm then the force constant is

Important Questions on Oscillations

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The restoring force of a system of mass executing SHM is $4 N$ . If its displacement is $4 cm$ then the force constant is