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The variation of amplitude of forced oscillation vs driving frequency, which point represents the heavy damping.

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Important Questions on Simple Harmonic Motion

EASY
What do you understand by free vibrations of a body?
EASY
Two pendulums C and D are suspended from a wire as shown in the given figure. Pendulum C is made to oscillate by displacing it from its mean position. It is seen that D also starts oscillating. Name the type of oscillation, C will execute.
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EASY
Why does the amplitude of a vibrating body continuously decrease during damped vibrations?
EASY
In case of a forced vibration, the resonance wave becomes very sharp when the:
HARD
A simple harmonic oscillator of angular frequency 2 rad s-1 is acted upon by an external force F=sint NIf the oscillator is at rest in its equilibrium position at t=0, its position at later times is proportional to:
EASY
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
EASY

Two pendulums C and D are suspended from a wire as shown in the given figure. Pendulum C is made to oscillate by displacing it from its mean position. It is seen that D also starts oscillating. If the length of D is made equal to C, then what difference will you notice in the oscillations of D

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EASY
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-
MEDIUM
A resonance tube is old and has a jagged end. It is still used in the laboratory to determine the velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to
MEDIUM
A stretched wire vibrates with a frequency of 60 Hz when the tension in the wire is T1 and with a frequency of 130 Hz when the tension in the wire is T2. If the tension in the wire is T1+T2, its frequency of vibration is
HARD
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 =103 kg m-3)
EASY
A tuning fork is used to produce resonance in glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27 oC two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27 oC is
MEDIUM
The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will decrease to α times its original magnitude, where α equals :
EASY
Consider a driven damped mechanical oscillator is in resonance. Which of the following statements is true ?
HARD

A pendulum with the time period of 1 s is losing energy due to damping. At a certain time, its energy is 45 J. If after completing 15 oscillations its energy has become 15 J, then its damping constant (in s-1) will be

MEDIUM
A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to 11000 of the original amplitude is close to:
EASY

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).

EASY
An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50cm . The next larger length of the column resonating with the same tuning fork is:
EASY

Two pendulums C and D are suspended from a wire as shown in the given figure. Pendulum C is made to oscillate by displacing it from its mean position. It is seen that D also starts oscillating. Name the type of oscillation, D will execute.

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