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 )

EASY

Earn 100

Define periodic motion

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

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

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

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:

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

For a simple pendulum, a graph is plotted between its kinetic energy (K.E.) and potential energy (P.E.) against its displacement d. which one of the following represents these correctly? (graphs are schematic and not drawn to scale)

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 block with mass

M

is connected by a massless spring with stiffness constant

k

to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude

A

about an equilibrium position

x_{0}

. Consider two cases : (i) when the block is at

x_{0}

and (ii) when the block is at

x = x_{0} + A

. In both the cases, a particle with mass

m (< M)

is softly placed on the block after which they stick to each other. Which of the following statement(s) is(are) true about the motion after the mass

m

is placed on the mass

M

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.]

HARD

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

A cylindrical plastic bottle of negligible mass is filled with

310 ml

of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency

ω .

If the radius of the bottle is

2 .5 cm

then

ω

is close to:

(

density of water

= 10^{3} kg m^{- 3})

MEDIUM

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

A particle is executing simple harmonic motion

(S H M)

of amplitude

A,

along the

x

-axis, about

x = 0 .

When its potential Energy

(P E)

equals kinetic energy

(K E),

the position of the particle will be:

MEDIUM

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

Two light identical springs of spring constant

k

are attached horizontally at the two ends of a uniform horizontal rod

A B

of length

l

and mass

m .

The rod is pivoted at its center 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is:
Question Image

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

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:

Define periodic motion

Important Questions on Oscillations

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