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Figure shows a torsional pendulum consists of a uniform disc $D$ of mass $M$ and radius $R$ attached to this rod of torsional constant $C .$ The energy of small torsional oscillations of the disc, if initially the disc was imparted angular speed $ω_{0},$ is given by $\frac{1}{n} M R^{2} {ω_{0}}^{2} .$ Find $n .$

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Important Questions on Oscillations

MEDIUM

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

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:

EASY

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

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

HARD

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

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}]

MEDIUM

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

Two simple pendulums of lengths in the ratio

4 : 1

start oscillating at

t = 0

. They will again be in phase after the shorter pendulum has made

n

oscillations. Find the value of

n

MEDIUM

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

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>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

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

MEDIUM

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

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>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

A bob of mass

m

suspended by a thread of length

ℓ

undergoes simple harmonic oscillations with time period

T .

If the bob is immersed in a liquid that has density

\frac{1}{4}

times that of the bob and the length of the thread is increased by

{(\frac{1}{3})}^{r d}

of the original length, then the time period of the simple harmonic oscillations will be:

EASY

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

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?

MEDIUM

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

A simple pendulum oscillating in air has period

T

. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is

\frac{1}{16} t h

of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:

EASY

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

When a simple pendulum is moved from the Earth's surface to deep mine, the period of oscillation

HARD

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

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

EASY

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

My friend has a Banjo clock. It has a pendulum. For every

1.0

sec the pendulum performs one full swing. If an object at the end of the string weighs

10.0 N

, what is the length of the pendulum?

EASY

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

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 :

MEDIUM

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

Two simple pendulums of length

1 m

each, with bobs having masses

1 kg

and

2 kg

, are hanging from the celling of an elevator. The elevator starts moving vertically downwards with acceleration

\frac{g}{10}

. Assuming

g = 10 m s^{- 2}

, approximately what are the time periods of the two pendulums?

MEDIUM

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

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

MEDIUM

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

If the length of the pendulum in pendulum clock increases by

0.1 %

, then the error in time per day is:

HARD

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

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

MEDIUM

Physics>Waves and Oscillations>Oscillations>Simple and Compound Pendulum

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>Simple and Compound Pendulum

The path length of oscillation of simple pendulum of length

1 m

16 cm

. Its maximum velocity is

(g = π^{2} {m s}^{-2})

Figure shows a torsional pendulum consists of a uniform disc D of mass M and radius R attached to this rod of torsional constant C. The energy of small torsional oscillations of the disc, if initially the disc was imparted angular speed ω0, is given by 1nMR2ω02. Find n.

Important Questions on Oscillations

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