Tag: free, forced and damped oscillations

Questions Related to free, forced and damped oscillations

The oscillation of a body or system with its own natural frequency and under no external influence other than the impulse that initiated the motion is known as:

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

  1. Damped oscillation

  2. Free oscillation

  3. Impulsive oscillation

  4. None of these

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Correct Option: B
Explanation:

The oscillation of a body or system with its own natural frequency and under no external influence other than the impulse that initiated the motion is known as free oscillation.

In case of forced oscillation, the resonance peak becomes very sharp when the

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

  1. restoring force is small.

  2. damping force is small.

  3. quality factor is small.

  4. applied periodic force is small.

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Correct Option: B
Explanation:

Lesser the damping force more sharp is the resonance peak.

At resonance, the amplitude of forced oscillations is

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

  1. minimum

  2. maximum

  3. zero

  4. none of these

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Correct Option: B
Explanation:

At resonance the amplitude of forced oscillations is maximum.

A particle of mass 0.10 kg executes Simple harmonic motion with an amplitude 0.05 m and frequency 20 vib/s. Its energy of oscillation is

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

  1. 2 J

  2. 4 J

  3. 1 J

  4. zero

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Correct Option: A
Explanation:

$E = \frac{1}{2}m{\omega^2}{A^2}$

$ = \frac{1}{2} \times 10 \times {\left( {2\pi  \times 20} \right)^2} \times {\left( {0.05} \right)^2}$
$ = 2J$
Hence,
option $(A)$ is correct answer.

The displacement of particle in S.H.M. is indicated by equation $y=10{\,}sin(20t+\pi/3)$where y is in meters. The value of time period of vibration will be (in seconds):

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

  1. $10/pi$

  2. $pi/10$

  3. $2\pi/10$

  4. $10/2\pi$

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Correct Option: A

A watch becomes fast by 5 minutes in a day. In the watch makers shop, it keeps correct time. It is due to :

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

  1. natural vibrations

  2. forced vibrations

  3. damped vibrations

  4. none of these

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Correct Option: B
Explanation:

In watchmakers' shop watch is oscillated with forced vibrations, so it has keeps correct time there. By itself, watch performs oscillations at natural frequency which is faster.

A wire stretched between two fixed supports, is plucked exactly in the middle and then released. It executes (neglect the resistance of the medium) :

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

  1. resonant vibrations

  2. free vibrations

  3. damped vibrations

  4. forced vibrations

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Correct Option: B
Explanation:

A wire stretched between two fixed supports, is plucked exactly in the middle and then released. It executes free vibrations.
Free vibrations are oscillations where the total energy stays the same over time. This means that the amplitude of the vibration stays the same. This is a theoretical idea because in real systems the energy is dissipated to the surroundings over time and the amplitude decays away to zero. This dissipation of energy is called damping.

A transverse wave is passing through a medium. The maximum speed of the vibrating particle occurs when the displacement of the particle from the mean position is

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

  1. zero

  2. half of the amplitude

  3. equal to the amplitude

  4. none of the above

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Correct Option: A
Explanation:

The maximum speed of the vibrating particle is when particle is on mean position.
In general total energy of the system remains constant. At the mean position potential energy is minimum this implies that kinetic energy will be maximum. Hence speed will be maximum. 

The vibrations of a body which take place under the influence of an external periodic force acting 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

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Correct Option: A
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 A. 

A simple pendulum of length 4 m is taken to a height $R$ (radius of the earth) from the earth's surface.The time period of small oscillations of the pendulum is $(g _{surface}={\pi}^{2 } m{s}^{-2})$

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

  1. 2 s

  2. 4 s

  3. 8 s

  4. 16 s

Show answer
Correct Option: C
Explanation:

The acceleration due to gravity of earth at a high 'h' 

${g} _{h} = {g} _{surface}\left( 1+\dfrac { h }{ R }  \right) ^{ -2 }$
g = acceleration due to surface gravity at earth surface
Now h = R (given)
so, ${g} _{h} = \dfrac { { g } _{ surface } }{ 4 } $
Now the time period of simple pendulum of length 4m at earth surface is 
${ T } _{ surface }=2\pi \sqrt { \dfrac { l }{ { g } _{ surface } }  } =2\pi \sqrt { \dfrac { 4 }{ 9.8 }  } \approx 4sec$
So time period at hight 'h = 2R' is 
$T=2\pi \sqrt { \dfrac { l }{ g _h }  } =2\pi \sqrt { \dfrac { 4\times 4 }{ { g } _{ surface } }  } =8sec$