HARD

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A horizontal cylinder closed at one end contains an ideal gas which is compressed by a tight-fitting and frictionless piston. The piston is connected to the other closed end of the cylinder via a spring with spring constant $k$ . The piston is of cross-sectional area $A$ and mass $M$ . In equilibrium, the chamber containing the gas has pressure $P$ and length $L$ while the spring is compressed by $l$ . Let the the piston be displaced by $d (≪ L)$ towards the vacuum region, and released. Choose the correct statement(s) regarding the oscillations of the piston by assuming all processes are isothermal.

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Important Questions on Simple Harmonic Motion

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

Two blocks of masses

m_{1} = 1 kg

and

m_{2} = 2 kg

are connected by a spring of spring constant

24 N m^{- 1}

and is placed on a horizontal frictionless surface. The block

m_{1}

is imparted an initial velocity

12 cm s^{- 1}

which produces maximum compression in the spring towards

m_{2}

. The amplitude of oscillation is

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

A spring whose unstrentches length is

l

has a force constant

k .

The spring is cut into two pieces of unstretches lengths

l_{1}

and

l_{2}

where,

l_{1} = n l_{2}

and

n

is an integer. The ratio

k_{1} / k_{2}

of the corresponding force constants,

k_{1}

and

k_{2}

will be:

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

A particle of mass $m$ is attached to four springs with spring constant $k, k, 2 k$ and $2 k$ as shown in the figure. Four springs are attached to the four corners of a square and a particle is placed at the center. If the particle is pushed slightly towards any side of the square and released, the period of oscillation will be

Question Image

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

A mass

M

is suspended from a light spring. An additional mass $m$ added displaces the spring further by a distance

X .

Now the combined mass will oscillate on the spring with period

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

A spring mass system (mass

m,

spring constant

k

and natural length

l

) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system rotates about it's axis with an angular velocity

ω, (k > > m ω^{2})

the relative change in the length of the spring is best given by the option:

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

10 Kg

collar is attached to a spring (spring constant

600 N / m

). It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by

20 cm

and released. What is the speed of the oscillation?

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

A tray of mass $12 kg$ is supported by two identical springs as shown in figure. When the tray is pressed down slightly and then released, it executes SHM with a time period of $1.5 s$ . The spring constant of each spring is

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MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

If two similar springs each of spring constant

K_{1}

are joined in series, the new spring constant and time period would be changed by a factor:

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

Two bodies of masses

1 kg

and

4 kg

are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency

25 rad s^{- 1}

, and amplitude

1.6 cm

while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take

g = 10 m s^{- 2}

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of

10^{12} s^{- 1}

. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver,

= 108 g {mol}^{- 1}

and Avogadro number

= 6.02 \times 10^{23}

)

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

In the given figure, a mass $M$ is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is $k .$ The mass oscillates on a frictionless surface with time period $T$ and amplitude $A .$ When the mass is in equilibrium position, as shown in the figure, another mass $m$ is gently fixed upon it. The new amplitude of oscillation will be:

Question Image

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

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

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

In the given figure, a body of mass $M$ is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant $k,$ the frequency of oscillation of given body is:

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HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

An arrangement of spring, strings, pulley and masses is shown in the figure below.
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The pulley and the strings are massless and

M > m

. The spring is light with spring constant

k

. If the string connecting

m

to the ground is detached, then immediately after detachment

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

Two identical springs of spring constant $2 k$ are attached to a block of mass $m$ and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is :

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EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

A mass

2 kg

is suspended from two coupled springs connected in series. The force constants for springs are

24.5 N m^{- 1}

and

25.5 N m^{- 1}

. The time period of the suspended mass is

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

Two particles

A

and

B

of equal masses are suspended from two massless springs of spring constants

K_{1}

and

K_{2}

respectively.If the maximum velocities during oscillations are equal, the ratio of the amplitude of

A

and

B

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

A block of mass

2 M

is attached to a massless spring with spring-constant

k .

This block is connected to two other blocks of masses

M

and

2 M

using two massless pulleys and strings. The accelerations of the blocks are

a_{1}, a_{2}

and

a_{3}

as shown in figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is

x_{0} .

Which of the following option(s) is/are correct?
[

g

is the acceleration due to gravity. Neglect friction]

Question Image

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

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

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Linear SHM

A solid block on a frictionless surface is connected to two rigid supports on the left and right side by springs of spring constants $k$ and $4 k$ respectively as shown in the figure. The time spent by the block in a complete cycle of oscillation on the left and the right side of the equilibrium position are $t_{L}$ and $t_{R}$ respectively. Which of the following is correct?

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Important Questions on Simple Harmonic Motion

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