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What is the time period of a second pendulum?
(Write the numerical value in terms of SI unit of time).

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Important Questions on Oscillations

MEDIUM

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating 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

EASY

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating Systems

A simple pendulum of length

1 m

has mass

10 g

and oscillates freely with amplitude of

5 cm

. Calculate its potential energy at extreme position.

HARD

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating 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})

HARD

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating Systems

The bob of a swinging second pendulum (one whose time period is

2 s

) has a small speed

v_{0}

at its lowest point. Its height from this lowest point

2.25 s

after passing through it, is given by

HARD

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating 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

EASY

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating 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

MEDIUM

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating Systems

The length of the second’s pendulum in a clock is increased to

4

times its initial length. Calculate the number of oscillations completed by the new pendulum in one minute.

EASY

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating Systems

Time period of a simple pendulum is

T

inside a lift when the lift is stationary. If the lift moves upwards with an acceleration

\frac{g}{2}

, the time period of pendulum will be :

EASY

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating Systems

The bob of simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob get suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

MEDIUM

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating 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

MEDIUM

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating Systems

If the time period of a two meter long simple pendulum is

2 s

, the acceleration due to gravity at the place where pendulum is executing S.H.M. is:

MEDIUM

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating 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

EASY

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating Systems

Given below are two statements:
Statement $I$ : A second's pendulum has a time period of $1$ second.

Statement $II$ : It takes precisely one second to move between the two extreme positions. In the light of the above statements,

choose the correct answer from the options given below

EASY

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating 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

EASY

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating Systems

The length of the seconds pendulum is

1 m

on earth. If the mass and diameter of the planet is

1.5

times that of the earth, the length of the seconds pendulum on the planet will be nearly

EASY

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating Systems

T_{0}

is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to

\frac{1}{16}

times of its initial value, the modified time period is

EASY

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating 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>Oscillations>Examples of Different Vibrating 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}]

EASY

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating Systems

In an experiment to determine the gravitational acceleration

g

of a place with the help of a simple pendulum, the measured time period squared is plotted against the string length of the pendulum in the figure. What is the value of

g

at the place?

HARD

Physics>Oscillations and Waves>Oscillations>Examples of Different Vibrating 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:
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What is the time period of a second pendulum? (Write the numerical value in terms of SI unit of time).

Important Questions on Oscillations

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What is the time period of a second pendulum?
(Write the numerical value in terms of SI unit of time).