Tag: free, forced and damped oscillations

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Questions Related to free, forced and damped oscillations

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

The oscillations of a pendulum about a vertical equilibrium position is an example of

  1. damped vibration

  2. free vibration

  3. forced vibration

  4. random vibration
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The oscillation of a pendulum about a vertical equilibrium position is an example of free vibration. As there no exciting force is present.

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

Which of the following is/are correct?

  1. The vibration of drilling machine depends on a force from outside

  2. The vibration of drilling machine does not depend on a force from outside

  3. When a pendulum vibrates it is free vibration because it does not depend on any outside force to vibrate

  4. When a pendulum vibrates it is free vibration because it depends on any outside force to vibrate
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

The correct statements are:

$A$ The vibration of drilling machine depends on the force from outside. Here the driven machine is driven by electricity.
$C$ When a pendulum vibrate it is free vibration because it does not depend upon any outside force to vibrate.

Multiple choice free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves 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.

  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} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Forced oscillations are described by a sinusoidal displacement function where the frequency matches the driving force frequency wd. Option A correctly represents the standard form of the displacement equation for a driven oscillator.

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

Forced oscillation is 

  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
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  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.
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. free vibrations

  2. damped vibrations

  3. natural vibrations

  4. None of these
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

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

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

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

  1. a damped vibration

  2. a forced vibration

  3. a mechanical vibration

  4. a transnational vinration
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. Tuning a radio

  2. Pipe instrument

  3. Rotating machinery

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. $d\frac { a }{ b }$
  2. $\dfrac { 2a }{ b } $
  3. $\dfrac { b }{a } $
  4. $\dfrac { b }{ 2a } $
Reveal answer Fill a bubble to check yourself
D Correct answer
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.