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Which of the following conditions is not sufficient for S.H.M. and why?

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Important Questions on Oscillations

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Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

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 :

MEDIUM

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

A rod of mass

M

and length

2 L

is suspended at its middle by a wire. It exhibits torsional oscillations. If two masses, each of mass

m

, are attached at a distance

L / 2

from its centre on both sides, it reduces the oscillation frequency by

20 %

. The value of ratio

m / M

is close to

HARD

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

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.]

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Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

A particle is executing SHM along a straight line. Its velocities at distances

x_{1}

and

x_{2}

from the mean position are

V_{1}

and

V_{2}

respectively. Its time period is:

HARD

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

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:

EASY

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

A tunnel is dug along the diameter of the earth. A mass

m

is dropped into it. How much time does it take to cross the earth?

EASY

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

A particle is executing a simple harmonic motion. Its maximum acceleration is

α

and maximum velocity is

β

. Then, its time period of vibration will be:

MEDIUM

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

A particle is executing simple harmonic motion with a time period

T

. At time

t = 0

, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like:

MEDIUM

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

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

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Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

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:

HARD

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

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>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

For particle $P$ revolving round the centre $O$ with radius of circular path $r$ and regular velocity $ω$ , as shown in below figure, the projection of $O P$ on the $x$ -axis at time $t$ is

Question Image

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Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

A body of mass,

m

is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass

m

is slightly pulled down and released, it oscillates with a time period of

3 s

. When the mass

m

is increased by

1 kg

, the time period of oscillations becomes

5 s

. The value of

m

kg

EASY

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

Which of the following plots represents schematically the dependence of the time period of a pendulum if measured and plotted as a function of its oscillations? (Note: amplitude need not be small)

MEDIUM

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

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>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

A simple pendulum of length

L

has mass

M

and it oscillates freely with amplitude

A

. At the extreme position, its potential energy is (

g

= acceleration due to gravity)

EASY

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

A particle is performing SHM starting from extreme position. Graphical representation shows that, between displacement and acceleration, there is a phase difference of

MEDIUM

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

The position co-ordinates of a particle moving in a $3 D$ coordinate system is given by

$x = a \cos ω t$

$y = a \sin ω t$

and $z = a ω t$

The speed of the particle is:

HARD

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

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)

MEDIUM

Physics>Waves and Oscillations>Oscillations>S.H.M. as Projection of U.C.M. Along any Diameter

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to

A

and

T

, respectively. At time

t = 0

one particle has displacement

A

while the other one has displacement

- \frac{A}{2}

and they are moving towards each other. If they cross each other at time

t

, then

t

is:

Which of the following conditions is not sufficient for S.H.M. and why?

Important Questions on Oscillations

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