Tag: physics

Questions Related to physics

If ${\omega} _d$ is a frequency of a driving force, then forced oscillations can be described by which of the following?  $b=$ least damping.

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

  1. $x(t)= A({\omega} _d/\omega , \ b) cos({\omega} _d t+ \phi)$

  2. $x(t)= A({\omega} _d/\omega , \ b) cos({\omega} _d )$

  3. $x(t) = A sin\theta + B cos\theta $

  4. $x(t) = \sqrt{A sin\theta + B cos\theta} $

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Correct Option: A

Forced oscillation is 

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

  1. simple harmonic motion but driven externally

  2. simple harmonic motion without driven externally

  3. having resonance when the driving frequency is the same as the natural frequency of the swing.

  4. Both A and C

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Correct Option: D
Explanation:

The force oscillation is (1) a simple harmonic motion driven by an external agency 

(ii) It has a resonance when the natural frequency of motion is equal to the driven frequency. 
At resonance the amplitude of motion and velocity of motion become maximum.

Which of the following is/are the correct option(s)?

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

  1. A louder sound is always produced when an accompanying object of smaller surface area is forced into vibration at the same natural frequency.

  2. A louder sound is always produced when an accompanying object of greater surface area is forced into vibration at the different natural frequency.

  3. A louder sound is always produced when an accompanying object of greater surface area is forced into vibration at the same natural frequency.

  4. A louder sound is always produced when an accompanying object of smaller surface area is forced into vibration at the different natural frequency.

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Correct Option: C
Explanation:

Statement C is true, consider the case of a guitar string mounted to the sound box. The fact that the sound box is greater than the surface area of the string means more surrounding particles will be forced into vibration causes an increase in amplitude and loudness.

The oscillations about a systems equilibrium position that occur in the absence of an external excitation are 

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

  1. free vibrations

  2. damped vibrations

  3. natural vibrations

  4. None of these

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Correct Option: A,C
Explanation:

The oscillations about a system of equilibrium position that occur in the absence of an external excitation are free vibrations or natural vibrations.

A person drives the paddle ball by moving his finger up and down at a certain frequency. In this example he is causing

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

  1. a damped vibration

  2. a forced vibration

  3. a mechanical vibration

  4. a transnational vinration

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Correct Option: B
Explanation:

A person drives the paddle ball by moving his finger up and down at a accelerating frequency. This is the example of force vibration as the motion of finger force to move paddle balls.

Which of the following is/are examples of forced oscillation?

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

  1. Tuning a radio

  2. Pipe instrument

  3. Rotating machinery

  4. All of the above

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Correct Option: D
Explanation:

(i) Tuning of Radio (ii) Pipe instrument (iii) Rotating machinery.

In all of the above cases system is exerted by an external force which causes its motion. So, are forced oscillation.

A driven oscillator is acted upon by a force $F={ F } _{ 0 }sin\ \omega $. The amplitude of oscillation is given by $A=\frac { { F } _{ 0 } }{ \sqrt { a{ \omega  }^{ 2\  }  -b\omega \ +c }} $, the resonant angular frequency is

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

  1. $d\frac { a }{ b }$

  2. $\dfrac { 2a }{ b } $

  3. $\dfrac { b }{a } $

  4. $\dfrac { b }{ 2a } $

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Correct Option: D
Explanation:

The driven force $ F= {F} _{0} \sin \omega t$

The amplitude of oscillation 
$A=\dfrac { { F } _{ 0 } }{ \sqrt { { a\omega  }^{ 2 }-b\omega +c }  } $
At resonance frequency A become maximum.So,
$\dfrac { dA }{ d\omega  } =0\ \Rightarrow { F } _{ 0 }\left( \dfrac { 2a\omega -b }{ \left( a{ \omega  }^{ 2 }-b\omega +1 \right)^{ \dfrac { 3 }{ 2 }}  }  \right) =0\ \Rightarrow \omega =\dfrac{b}{2a} \rightarrow$  
This is the resonence frequency.

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

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:

Force vibration is a type at vibration in which a body is vibrate without any external influence and vibrates with its natural frequency. So, given statement describes a free vibrations.


The vibrations which occur when work is being done on the system are called 

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

  1. free vibrations.

  2. forced vibrations.

  3. natural vibrations.

  4. random vibrations.

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Correct Option: B
Explanation:

The vibrations which occur when work is being done on the system is called forced vibration.

Motion of reciprocating pistons in engine is an example of

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

  1. Forced vibration

  2. Natural vibration

  3. Recursive vibration

  4. None of these

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Correct Option: A
Explanation:

A motion of reciprocating pistons in an engine is an example of force vibration. In this case motion of the piston is governed by a pressure of a gas inside ignition of a chamber.