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 )

HARD

Earn 100

A conducting rod $A B$ of mass $m$ and length $l$ is supported by conducting massless wires and carrying a current $I$ as shown in the figure. The rod is slightly displaced into the paper such that rod always remains parallel to $x$ -axis and released to perform SHM. If its time period is $2 π \sqrt{\frac{k a}{g}} {[1 + {(\frac{Bl l}{mg})}^{2}]}^{- 1 / 4}$ . Find the value of $k$ .

Important Questions on Oscillations

MEDIUM

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

An object was found to make oscillations governed by the equation

y = \cos^{2} (ω t + \frac{π}{4}) - 0.5

. The amplitude and angular frequency of these oscillations, respectively, are

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.]

EASY

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

A mass

M

is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes

S . H . M .

of period

T

. If the mass is increased by

m

, the time period becomes

\frac{5 T}{3} .

What is the ratio

(\frac{M}{m})

EASY

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

The function of time representing a simple harmonic motion with a period of

\frac{π}{ω}

is :

HARD

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

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

Question Image

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

MEDIUM

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

A body of mass

1 kg

is made to oscillate on a spring of force constant

15 N / m

. Calculate the angular frequency

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

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>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?

EASY

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

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

MEDIUM

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

A wave along a string has the following equation

y = 0.05 \sin (28 t - 1.78 x) m

(where,

t

is in seconds and

x

is in meters). What are the amplitude

(A),

frequency

(f)

and wavelength

(λ)

of the wave ?

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:

MEDIUM

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

A body of mass

1 kg

is made to oscillate on a spring of force constant

15 N / m

. Calculate the frequency of vibrations.

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

Two massless springs with spring constants

2 k

and

9 k

, carry

50 g

and

100 g

masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes 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

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

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:

Important Questions on Oscillations

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