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Find an expression for the time period of a vertical spring-mass system.

Important Questions on Oscillations

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Physics>Oscillations and Waves>Oscillations>Oscillating Systems

The time period of a bob performing simple harmonic motion in water is

2 s

. If density of bob is

\frac{4}{3} \times 10^{3} kg m^{- 3}

, then time period of bob performing simple harmonic motion in air will be

HARD

Physics>Oscillations and Waves>Oscillations>Oscillating Systems

Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulum is

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Physics>Oscillations and Waves>Oscillations>Oscillating Systems

Two simple pendulums of lengths

5 m

and

20 m

respectively are given small displacement in one direction at the same time they will again be in the same sense when the pendulum of shorter length has completed

n

oscillations. Then,

n

HARD

Physics>Oscillations and Waves>Oscillations>Oscillating Systems

A hollow sphere of radius

R

is suspended from a thin rod. If the sphere is twisted by a small angle about the wire axis and released, simple harmonic oscillation (SHM) will ensure with a period of

τ_{1}

. Now, if the hollow sphere is replaced by a solid sphere of radius and mass equal to that of a hollow sphere, the SHM will have a period

τ_{2}

. The ratio of time periods

(τ_{1} / τ_{2})

MEDIUM

Physics>Oscillations and Waves>Oscillations>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:

EASY

Physics>Oscillations and Waves>Oscillations>Oscillating Systems

Two clocks

A

and

B

are synchronized to show the same time on earth. Clock

A

is based on oscillations of spring and clock

B

is based on a pendulum motion. If these two clocks are taken to the surface of the moon, then

HARD

Physics>Oscillations and Waves>Oscillations>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

HARD

Physics>Oscillations and Waves>Oscillations>Oscillating Systems

The path length of oscillation of simple pendulum of length

1 m

16 cm

. Its maximum velocity is

(g = π^{2} {m s}^{-2})

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Physics>Oscillations and Waves>Oscillations>Oscillating Systems

1 kg

block attached to a spring vibrates with a frequency of

1 Hz

on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to a

8 kg

block placed on the same table. So, the frequency of vibration of the

8 kg

block is

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Physics>Oscillations and Waves>Oscillations>Oscillating Systems

In an experiment to determine the period of a simple pendulum of length

1 m

, it is attached to different spherical bobs of radii

r_{1}

and

r_{2}

. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be

5 \times 10^{- 4} s

, the difference in radii,

|r_{1} - r_{2}|

is best-given by

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Physics>Oscillations and Waves>Oscillations>Oscillating Systems

A pendulum has length of

0.4 m

and maximum speed

4 m s^{- 1}

. When the length makes an angle

30 °

with the horizontal, its speed will be

[\sin \frac{π}{6} = \cos \frac{π}{3} = 0.5

and

g = 10 m s^{- 2}]

HARD

Physics>Oscillations and Waves>Oscillations>Oscillating Systems

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.

EASY

Physics>Oscillations and Waves>Oscillations>Oscillating Systems

A simple pendulum has time period $T_{1}$ . The point of suspension is now moved upward according to the relation $y = k t^{2}, (k = 1 m s^{- 2})$ where $y$ is the vertical displacement. The time
period now becomes $T_{2}$ .

The ratio of $\frac{T_{1}^{2}}{T_{2}^{2}} (g = 10 m s^{- 2})$ is

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Physics>Oscillations and Waves>Oscillations>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)

EASY

Physics>Oscillations and Waves>Oscillations>Oscillating Systems

A spring of force constant

k

is cut into lengths of ratio

1 : 2 : 3

. They are connected in series and the new force constant is

k'

. If now they are connected in parallel and force constant is

k''

, then

k' : k''

HARD

Physics>Oscillations and Waves>Oscillations>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})

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Physics>Oscillations and Waves>Oscillations>Oscillating Systems

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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HARD

Physics>Oscillations and Waves>Oscillations>Oscillating Systems

The time period for small vertical oscillations of a block of mass $m$ when the masses of the pulleys are negligible and spring constant $k_{1}$ and $k_{2}$ is

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Physics>Oscillations and Waves>Oscillations>Oscillating Systems

A $10 kg$ body is suspended from an ideal spring (force constant $250 {Nm}^{- 1}$ .) How much time it will take in reaching its mean position from its position of maximum displacement?

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Physics>Oscillations and Waves>Oscillations>Oscillating Systems

A system is shown in the figure. The time period for small oscillations of the two blocks will be

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Find an expression for the time period of a vertical spring-mass system.

Important Questions on Oscillations

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