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What is the number of degrees of freedom for an oscillating simple pendulum?

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Important Questions on Simple Harmonic Motion

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Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple 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>Oscillations and Waves>Simple Harmonic Motion>Simple 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>Oscillations and Waves>Simple Harmonic Motion>Simple 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>Oscillations and Waves>Simple Harmonic Motion>Simple 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>Oscillations and Waves>Simple Harmonic Motion>Simple 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 :

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple 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?

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple 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

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple 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

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple 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>Oscillations and Waves>Simple Harmonic Motion>Simple 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>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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

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Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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>Simple Harmonic Motion>Simple 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?

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple 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:

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

If the length of the pendulum in pendulum clock increases by

0.1 %

, then the error in time per day is:

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple 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

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple 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?

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

A tunnel is dug along the diameter of the earth. A mass

m

is dropped into it. How much time does it take to cross the earth?

What is the number of degrees of freedom for an oscillating simple pendulum?

Important Questions on Simple Harmonic Motion

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