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The equation of motion for pendulum is

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Important Questions on Oscillations

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

The system that returns to equilibrium as quickly as possible without oscillating is

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

The amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass

= 500 g

, Decay constant

= 20 g s^{- 1}

then how much time is required for the amplitude of the system to drop to half of its initial value?

(\ln 2 = 0.693)

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

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

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

Two simple pendulums with time periods

T_{0}

and

T_{1}

start oscillating in the same direction at the same time. If

T_{0} > T_{1}

and the phase difference between them is

\frac{π}{3}

when the faster pendulum has completed one oscillation, then

T_{1}

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

The displacement of a damped harmonic oscillator is given by

x (t) = e^{- 0.1 t} \cos (10 π t + φ) .

Here

t

is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to:

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

The phenomenon that occurs when the frequency of forced vibrations on an object matches the natural frequency of that object, and produces a dramatic increase in amplitude is called

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

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

HARD

Physics>Advanced Mechanics>Oscillations>Energy in SHM

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>Advanced Mechanics>Oscillations>Energy in SHM

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

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

A block of mass

1 kg

attached to a spring is made to oscillate with an initial amplitude of

12 cm

. After

2

minutes the amplitude decreases to

6 cm

. Determine the value of the damping constant for this motion. (take

\ln 2 = 0.693

)

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

In case of a forced vibration, the resonance wave becomes very sharp when the:

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 5 = 1.601, ln 2 = 0.693).

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

A simple pendulum is oscillating in a lift. If the lift starts moving upwards with uniform acceleration, the period _____.

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

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?

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

Time period of a simple pendulum in a stationary lift is

T

. If the lift accelerates with

\frac{g}{6}

vertically upwards then the time period will be
(Where

g =

acceleration due to gravity)

MEDIUM

Physics>Advanced Mechanics>Oscillations>Energy in SHM

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>Advanced Mechanics>Oscillations>Energy in SHM

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?

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

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 :

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

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?

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Physics>Advanced Mechanics>Oscillations>Energy in SHM

A block of mass

0.1 kg

is connected to an elastic spring of spring constant

640 N m^{- 1}

and oscillates in a damping medium of damping constant

10^{- 2} kg s^{- 1}

. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to-

The equation of motion for pendulum is

Important Questions on Oscillations

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