Tag: free, forced and damped oscillations

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

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:

  1. Damped oscillation

  2. Free oscillation

  3. Impulsive oscillation

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. 2 J

  2. 4 J

  3. 1 J

  4. zero
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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):

  1. $10/pi$
  2. $pi/10$
  3. $2\pi/10$
  4. $10/2\pi$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Comparing the given equation y = 10 sin(20t + pi/3) with the standard SHM equation y = A sin(omega*t + phi), we find the angular frequency omega = 20 rad/s. The time period T is given by 2*pi / omega, which equals 2*pi / 20 = pi/10 seconds.

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

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

  1. natural vibrations

  2. forced vibrations

  3. damped vibrations

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. resonant vibrations

  2. free vibrations

  3. damped vibrations

  4. forced vibrations
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. zero

  2. half of the amplitude

  3. equal to the amplitude

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
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. 

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

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

  1. Forced vibrations

  2. Free vibration

  3. Damped vibrations

  4. All
Reveal answer Fill a bubble to check yourself
A Correct answer
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. 

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

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 $(g _{surface}={\pi}^{2 } m{s}^{-2})$

  1. 2 s

  2. 4 s

  3. 8 s

  4. 16 s
Reveal answer Fill a bubble to check yourself
C Correct answer
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 
$T=2\pi \sqrt { \dfrac { l }{ g _h }  } =2\pi \sqrt { \dfrac { 4\times 4 }{ { g } _{ surface } }  } =8sec$