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 )

The displacement-time graph for a particle executing SHM is as shown in figure. Which of the following statements is correct?

The velocity of the particle is maximum at t = 3 4 T .

The velocity of the particle is maximum at t = T 2 .

The acceleration of the particle is maximum at t = T 4 .

The acceleration of the particle is maximum at t = 3 4 T .

EASY

Earn 100

Is acceleration maximum at extreme position in SHM?

Important Questions on Oscillations

HARD

Physics>Waves and Oscillations>Oscillations>Phase of S.H.M

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 _____ .

EASY

Physics>Waves and Oscillations>Oscillations>Phase of S.H.M

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

EASY

Physics>Waves and Oscillations>Oscillations>Phase of S.H.M

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>Waves and Oscillations>Oscillations>Phase of S.H.M

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

HARD

Physics>Waves and Oscillations>Oscillations>Phase of S.H.M

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

EASY

Physics>Waves and Oscillations>Oscillations>Phase of S.H.M

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

MEDIUM

Physics>Waves and Oscillations>Oscillations>Phase of S.H.M

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>Waves and Oscillations>Oscillations>Phase of S.H.M

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>Waves and Oscillations>Oscillations>Phase of S.H.M

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>Waves and Oscillations>Oscillations>Phase of S.H.M

The function

(\sin ω t - \cos ω t)

represents the S.H.M having a time period

T

HARD

Physics>Waves and Oscillations>Oscillations>Phase of S.H.M

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>Waves and Oscillations>Oscillations>Phase of S.H.M

When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be

EASY

Physics>Waves and Oscillations>Oscillations>Phase of S.H.M

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>Waves and Oscillations>Oscillations>Phase of S.H.M

A particle executes simple harmonic motion and it is located at