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A rod of length $l,$ mass m are connected to two springs of spring constant $K$ each. Find the frequency of small oscillation

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Important Questions on Simple Harmonic Motion

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Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

A cylindrical plastic bottle of negligible mass is filled with

310 ml

of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency

ω .

If the radius of the bottle is

2 .5 cm

then

ω

is close to:

(

density of water

= 10^{3} kg m^{- 3})

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

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

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

Two masses

m

and

\frac{m}{2}

are connected at the two ends of a massless rigid rod of length

l .

The rod is suspended by a thin wire of torsional constant

k

at the centre of mass of the rod-mass system (see figure). Because of torsional constant

k,

the restoring torque is

τ = k θ

for angular displacement

θ .

If the rod is rotated by

θ_{0}

and released, the tension in it when it passes through its mean position will be:
Question Image

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

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}

)

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

Naturally oscillating systems undergo

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

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>Oscillating Systems

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

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

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>Oscillating Systems

What is the time period of the pendulum in a lift, which is falling freely under gravity

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

A car is moving on a plane inclined at

30 °

to the horizontal with an acceleration of

10 {m s}^{- 2}

parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is (Take

g = 10 {m s}^{- 2}

)

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

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:

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

A cylindrical block of wood of mass

10 kg

and radius

10 cm

is floating in water with its axis vertical. When it is depressed a little and then released, it starts executing simple hormonic motion (SHM). The frequency of the SHM, executed by the block is:
(Assume

g = 10 m s^{- 2}

and let

ρ

is the density of the water)

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

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:

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

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>Oscillating Systems

If the mass shown in figure is slightly displaced and then let go, then the system shall oscillate with a time period of
Question Image

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

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

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

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>Oscillating Systems

The time period of oscillation of a simple pendulum of length

L

suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination

α

, is given by :

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

The time period of a simple pendulum inside a stationary lift is

T

. If the lift starts moving upwards with an acceleration of

\frac{g}{3}

, its time period will be,

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Oscillating Systems

A rectangular block of mass

m

and area of cross-section

A

floats in a liquid of density

ρ

. If it is given a vertical displacement from equilibrium, it undergoes oscillation with a time period

T

. Then

A rod of length l, mass m are connected to two springs of spring constant K each. Find the frequency of small oscillation

Important Questions on Simple Harmonic Motion

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A rod of length $l,$ mass m are connected to two springs of spring constant $K$ each. Find the frequency of small oscillation