Tag: oscillations

Questions Related to oscillations

Equations y = 2A cos$^{2}$ $\omega $t and y = A (sin $\omega $  + $\sqrt{3}$ cos $\omega $t  ) represent the motion of two particles.

resonance oscillations physics

  1. Only one of these is S.H.M.

  2. Ratio of maximum speeds is 2 : 1

  3. Ratio of maximum speeds is 1 : 1

  4. Ratio of maximum accelerations is 1 : 4

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Correct Option: C

Your friend is playing a song on a piano. Whenever your friend hits a certain key, the lamp on top of the piano rattles. Explain why the lamp rattles.

resonance oscillations physics

  1. The lamp rattles because of the occurring of interference 

  2. The lamp rattles because of the occurring of diffraction 

  3. The lamp rattles because of the occurring of resonance

  4. None of the above 

Show answer
Correct Option: C
Explanation:

This happens due to resonance (A phenomenon in which a vibrating system or external force drives another system to oscillate with a greater amplitude at a specific frequency). The lamp on top of the piano has a resonant frequency equal to one of the notes being played.

During resonance, sound waves tend to absorb

resonance oscillations physics

  1. more energy

  2. less energy

  3. no energy

  4. infinite energy

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Correct Option: A
Explanation:

System to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies.

A glass tube of $1.0 m$ length is filled with water. The water can be drained out slowly at bottom of the tube. If a vibrating turning fork of frequency $500 Hz$ is brought at the upper end of the tube and the velocity of sound is $330 \,\,m\,\,s^{-1}$, then the total number of resonances obtained will be:

resonance oscillations physics

  1. 4

  2. 3

  3. 2

  4. 1

Show answer
Correct Option: B
Explanation:

Wavelength of the sound produced is,
$\lambda = \dfrac{Velocity}{Frequency} $


$= \dfrac{330\,\,m\,\,s^{-1}}{500\,\,s^{-1}} = 0.66\,\,m$
The resonance occurs at
$\dfrac{\lambda}{4},\dfrac{3\lambda}{4},\dfrac{5\lambda}{4},\dfrac{7\lambda}{4},.....$
i.e., at $0.165\,\,m, 0.495\,\,m, 0.825\,\,m, 1.155\,\,m$. As the length of the tube is only $1.0\,\,m$, hence $3$ resonance will be observed.

$mx^{2} - bx + k = 0$. Find time after which to the energy will become half of initial maximum value in damped forced oscillation.

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. $t = \dfrac {m}{b} + \dfrac {1}{2} ln2$

  2. $t = \dfrac {m}{b} \times \dfrac {2}{3} ln2$

  3. $t = \dfrac {m}{b} - \dfrac {1}{2} ln2$

  4. $t = \dfrac {m}{b} \times \dfrac {1}{2} ln2$

Show answer
Correct Option: D
Explanation:

$\dfrac {1}{\sqrt {2}} = e^{-bt/m}$
$ln \sqrt {2} = \dfrac {bt}{m}$
$t = \dfrac {m}{b} \times \dfrac {1}{2} ln2$.

The periodic vibrations of a body of constant amplitude in the absence of any external force on it are called

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. Forced vibrations

  2. Free vibration

  3. Damped vibrations

  4. All

Show answer
Correct Option: B
Explanation:

Forced vibrations: External force is acting on the body. 
Free vibration: Constant amplitude and no external force.
Damped vibration: Amplitude is not constant, it keeps on decreasing due to environmental factors of the system like air resistance.  
Therefore, correct option is B. 

The tendency of one object to force another adjoining or interconnected object into vibration motion is referred to as a 

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. forced vibration.

  2. damped vibration

  3. loudness

  4. pitch

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Correct Option: A
Explanation:

The tendency of one object to force another adjoining or interconnected object into vibrating motion is referred to as a forced oscillation.

If a force is continually or repeatedly applied to keep the oscillation going, it is called 

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. forced oscillator.

  2. free oscillatior

  3. damped oscillatior

  4. none of the above

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Correct Option: A
Explanation:

When a periodically repetitive and oscillatory force acts on an object, then the object is forced to oscillate with the frequency of the periodic force. Such oscillation is known as forced oscillation. When an object is displaced from its mean position and allowed to vibrate along its mean position then the object vibrates with its own natural frequency. This is known as free vibration or oscillation. And an oscillation in which the amplitude goes on decreasing with time is known as damped oscillation.

When we push a child in a swing, the amplitude of the oscillation

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. decreases

  2. increases

  3. remains same

  4. none of the above

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Correct Option: B
Explanation:

By pushing a child on a swing a driving force is applied which forces the swing and the child in the forward direction. The gravitational force acts as a restoring force and pulls back the child to the original position. These two forces together set them into an oscillatory motion. By pushing the child the amplitude, that is the maximum displacement, increases.

The orbital motion of the earth, around the sun is 

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. periodic but not oscillatory

  2. oscillatory but not periodic

  3. neither periodic not oscillatory

  4. both periodic and oscillatory

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Correct Option: A
Explanation:

The orbital motion of the earth around the sun is not an oscillatory motion as it is not a two and fro motion about a mean position. But it is a periodic motion.