Free, damped and forced oscillations - class-XI
free, damped and forced oscillations
Questions
$mx^{2} - bx + k = 0$. Find time after which to the energy will become half of initial maximum value in damped forced oscillation.
- $t = \dfrac {m}{b} + \dfrac {1}{2} ln2$
- $t = \dfrac {m}{b} \times \dfrac {2}{3} ln2$
- $t = \dfrac {m}{b} - \dfrac {1}{2} ln2$
- $t = \dfrac {m}{b} \times \dfrac {1}{2} ln2$
The periodic vibrations of a body of constant amplitude in the absence of any external force on it are called
- Forced vibrations
- Free vibration
- Damped vibrations
- All
The tendency of one object to force another adjoining or interconnected object into vibration motion is referred to as a
- forced vibration.
- damped vibration
- loudness
- pitch
If a force is continually or repeatedly applied to keep the oscillation going, it is called
- forced oscillator.
- free oscillatior
- damped oscillatior
- none of the above
When we push a child in a swing, the amplitude of the oscillation
- decreases
- increases
- remains same
- none of the above
Which of the following works on the principle of forced vibration?
- Guitar
- Tuning fork
- Drum
- All of the above
A motion caused by an unbalanced rotating component is an example of
- free vibration
- forced vibration
- natural vibration
- None of these
Resonance is an example of
- forced oscillation
- damped oscillation
- free oscillation
- none of these
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:
- Damped oscillation
- Free oscillation
- Impulsive oscillation
- None of these
In case of forced oscillation, the resonance peak becomes very sharp when the
- restoring force is small.
- damping force is small.
- quality factor is small.
- applied periodic force is small.
At resonance, the amplitude of forced oscillations is
- minimum
- maximum
- zero
- none of these
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
- 2 J
- 4 J
- 1 J
- zero
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):
- $10/pi$
- $pi/10$
- $2\pi/10$
- $10/2\pi$
A watch becomes fast by 5 minutes in a day. In the watch makers shop, it keeps correct time. It is due to :
- natural vibrations
- forced vibrations
- damped vibrations
- none of these
A wire stretched between two fixed supports, is plucked exactly in the middle and then released. It executes (neglect the resistance of the medium) :
- resonant vibrations
- free vibrations
- damped vibrations
- forced vibrations
The vibrations of a body which take place under the influence of an external periodic force acting on it are called
- Forced vibrations
- Free vibration
- Damped vibrations
- All
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 $(g _{surface}={\pi}^{2 } m{s}^{-2})$
- 2 s
- 4 s
- 8 s
- 16 s
The oscillations of a pendulum about a vertical equilibrium position is an example of
- damped vibration
- free vibration
- forced vibration
- random vibration
Which of the following is/are correct?
- The vibration of drilling machine depends on a force from outside
- The vibration of drilling machine does not depend on a force from outside
- When a pendulum vibrates it is free vibration because it does not depend on any outside force to vibrate
- When a pendulum vibrates it is free vibration because it depends on any outside force to vibrate
If ${\omega} _d$ is a frequency of a driving force, then forced oscillations can be described by which of the following? $b=$ least damping.
- $x(t)= A({\omega} _d/\omega , \ b) cos({\omega} _d t+ \phi)$
- $x(t)= A({\omega} _d/\omega , \ b) cos({\omega} _d )$
- $x(t) = A sin\theta + B cos\theta $
- $x(t) = \sqrt{A sin\theta + B cos\theta} $
Forced oscillation is
- simple harmonic motion but driven externally
- simple harmonic motion without driven externally
- having resonance when the driving frequency is the same as the natural frequency of the swing.
- Both A and C
The oscillations about a systems equilibrium position that occur in the absence of an external excitation are
- free vibrations
- damped vibrations
- natural vibrations
- None of these
A person drives the paddle ball by moving his finger up and down at a certain frequency. In this example he is causing
- a damped vibration
- a forced vibration
- a mechanical vibration
- a transnational vinration
Which of the following is/are examples of forced oscillation?
- Tuning a radio
- Pipe instrument
- Rotating machinery
- All of the above
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
- $d\frac { a }{ b }$
- $\dfrac { 2a }{ b } $
- $\dfrac { b }{a } $
- $\dfrac { b }{ 2a } $
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
- Damped oscillation
- Free oscillation
- Impulsive oscillation
- None of these
The vibrations which occur when work is being done on the system are called
- free vibrations.
- forced vibrations.
- natural vibrations.
- random vibrations.
Motion of reciprocating pistons in engine is an example of
- Forced vibration
- Natural vibration
- Recursive vibration
- None of these
The motion of a vehicle suspension system just after the vehicle encounters a pothole is an example of
- natural vibration
- damped vibration
- forced vibration
- None of these
Assertion : A child in a garden swing periodically presses his feet against the ground to maintain the oscillations.
Reason : Then all free oscillations eventually die out because of the ever present damping force.
- If both assertion and reason are true and reason is the correct explanation of assertion.
- If both assertion and reason are true and reason is not the correct explanation of assertion.
- If assertion is true but reason is false.
- If both assertion and reason are false.
A linear harmonic oscillator of force constant $2 \times$10$^{6}$Nm$^{-1}$ and amplitude 0.01 m has a total mechanical energy of 160 J. Its
- maximum potential energy is 100 J
- maximum kinetic energy is 100 J
- maximum potential energy is 160 J
- minimum potential energy is zero.