MEDIUM

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What is the difference between periodic motion and SHM?

Important Questions on Oscillations

HARD

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

One end of a spring of negligible unstretched length and spring constant $k$ is fixed at the origin $(0, 0)$ . A point particle of mass $m$ carrying a positive charge $q$ is attached at its other end. The entire system is kept on a smooth horizontal surface. When a point dipole $\vec{p}$ pointing towards the charge $q$ is fixed at the origin, the spring gets stretched to a length $l$ and attains a new equilibrium position (see figure below). If the point mass is now displaced slightly by $Δ l ≪ l$ from its equilibrium position and released, it is found to oscillate at frequency $\frac{1}{δ} \sqrt{\frac{k}{m}},$ The value of $δ$ is _______.

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EASY

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

A body is in simple harmonic motion with time period

T = 0.5 s

and amplitude

A = 1 cm

. Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.

HARD

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

A perfectly reflecting mirror of mass

M

mounted on a spring constitutes a spring-mass system of angular frequency

Ω

such that

\frac{4 π M Ω}{h} = 10^{24} m^{- 2}

with

h

as Planck's constant.

N

photons of wavelength

λ = 8 π \times 10^{- 6} m

strike the mirror simultaneously at normal incidence such that the mirror gets displaced by

1 μ m .

If the value of

N

x \times 10^{12},

then the value of

x

is________.
[Consider the spring as massless]

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MEDIUM

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

When a body is in $S H M$ , then match the following.

$List - I$		$List - II$
$(A)$	Velocity is maximum	$(I)$	Acceleration is maximum
$(B)$	$KE$ is ${(\frac{3}{4})}^{th}$ of total energy	$(II)$	At mean position
$(C)$	$PE$ is ${(\frac{3}{4})}^{th}$ of total energy	$(III)$	At half of the amplitude
$(D)$	Acceleration is maximum	$(IV)$	At $\frac{\sqrt{3}}{2}$ times the amplitude

HARD

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

A particle of mass

m

is attached to one end of a massless spring of force constant

k

, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time

t = 0

with an initial velocity

u_{0}

. When the speed of the particle is

0.5 u_{0}

, it collides elastically with a rigid wall. After this collision :

EASY

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

x, v

and

a

denote the displacement, the velocity and the acceleration of a particle executing

S H M

of time period

T

. Then, which of the following does not change with time?

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)

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EASY

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

A pendulum oscillates simple harmonically and only if
i. The size of the bob of pendulum is negligible in comparison with the length of the pendulum
ii. The angular amplitude is less than

15 °

MEDIUM

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

A simple pendulum is attached to a block which slides without friction down an inclined plane $(A B C)$ having an angle of inclination $α$ as shown while the block is sliding down the pendulum oscillates in such a way that at its mean position the direction of the string is,

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HARD

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

A simple pendulum of length $l$ is made to oscillate with amplitude of $45$ degrees. The acceleration due to gravity is $g$ . Let $T_{0} = 2 π \sqrt{\frac{l}{g}} .$ The time period of oscillation of this pendulum will be

EASY

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

In the case of a simple pendulum executing

SHM,

t = 0

, the bob is not at the mean position. The graph drawn between the tension

(T)

in the string and time

(t)

MEDIUM

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

A light balloon filled with helium of density,

ρ_{H e}

is tied to a long light string of length,

l

and the string is attached to the ground. If the balloon is displaced slightly in the horizontal direction from the equilibrium and released then.

EASY

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

Y = A \sin (ω t + ϕ_{0})

is the time-displacement equation of a

S H M .

t = 0

the displacement of the particle is

Y = \frac{A}{2}

and it is moving along negative

x

-direction. Then the initial phase angle

ϕ_{0}

will be:

MEDIUM

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

Identify the function which represents a periodic motion

MEDIUM

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

A particle is making simple harmonic motion along the

X

-axis. If at a distances

x_{1}

and

x_{2}

from the mean position the velocities of the particle are

v_{1}

and

v_{2}

, respectively. The time period of its oscillation is given as:

EASY

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

A hole is drilled along the diameter of the earth and a stone is dropped into it. Then the stone

EASY

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

One end of a rod of length $L$ is fixed to a point on the circumference of a wheel of radius $R$ . The other end is sliding freely along a straight channel passing through the centre $O$ of the wheel as shown in the figure below. The wheel is rotating with a constant angular velocity $ω$ about $O$ . Taking $T = \frac{2 π}{ω}$ , the motion of the rod is

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MEDIUM

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

A particle moves according to the law,

x = r c o s \frac{π t}{2}

. The distance covered by it the time interval between

t = 0 t o t = 3 s

MEDIUM

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

Many random snapshots using a camera are taken of a particle in simple harmonic motion between,

x = - x_{0}

and

x = + x_{0}

with origin

x = 0

as the mean position. A histogram of the total number of times the particle is recorded about a given position (event no) would most closely resemble,

HARD

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

A particle moves with simple harmonic motion in a straight line. In first

τ s

, after starting from rest it travels a distance a, and in next

τ s

it travels 2a, in same direction, then :

What is the difference between periodic motion and SHM?

Important Questions on Oscillations

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