Tag: damped harmonic motion

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Questions Related to damped harmonic motion

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

The phenomenon in which the amplitude of oscillation of a pendulum decreases gradually is called

  1. decay period of oscillation

  2. damping

  3. building up of oscillation

  4. maintained oscillation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Whenever there is a damping force, it will slow down the motion of a pendulum, and ultimately it will make the pendulum stop. This phenomenon is called damping.

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

The oscillations of a pendulum slow down due to :

  1. the force exerted by air and the force exerted by friction at the support

  2. the force exerted by air only

  3. the forces exerted by friction at the support

  4. they never slow down
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The pendulum on its motion has friction particle. As a result of this frictional force slows down.

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

In which of the following there is some loss of energy in the form of heat

  1. Forced vibrations

  2. Free vibration

  3. Damped vibrations

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

It is our common experience that when a body is made to vibrate in a medium , the amplitude of the vibrating body continuously decreases with time and ultimately the body stops vibrating.this is called the damped vibrations.

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

The periodic vibrations of a body of decreasing amplitude in the presence of resistive force on it are called

  1. Forced vibrations

  2. Free vibration

  3. Damped vibrations

  4. All
Reveal answer Fill a bubble to check yourself
C 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 C. 

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

Any oscillation in which the amplitude of the oscillating quantity decreases with time is termed as

  1. Damped oscillation

  2. Free oscillation

  3. Depletion oscillation

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

Any oscillation in which the amplitude of the oscillating quantity decreases with time is termed as damped oscilaation

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

The amplitude of a damped oscillator becomes $\dfrac {1}{27}$ of initial value after $6\ minutes$. Its amplitude after $2\ minutes$ is:

  1. $\dfrac {A _{0}}{3}$
  2. $\dfrac {A _{0}}{9}$
  3. $\dfrac {A _{0}}{54}$
  4. $\dfrac {A _{0}}{81}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a damped oscillator, amplitude A(t) = A0 * e^(-bt). Given A(6) = A0/27, we have e^(-6b) = 1/27, so e^(-2b) = (1/27)^(1/3) = 1/3. Thus, A(2) = A0 * e^(-2b) = A0/3.

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

In damped vibrations, as time progresses, amplitude of oscillation

  1. decreases

  2. increases

  3. Remains same

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In damped oscillations, the relation of amplitude of oscillations with time is given by $y={ y } _{ o }{ e }^{ -bt }=\frac { { y } _{ o } }{ { e }^{ -bt } } $, where
${ y } _{ o }=$ initial amplitude of oscillation
$t=$time
$b=$damping constant
since $b>0\quad & \quad t>0;$
${ e }^{ bt }>1\ { \Rightarrow e }^{ -bt }<1\ { \Rightarrow { y } _{ o }e }^{ -bt }<{ y } _{ o }\ \Rightarrow y<{ y } _{ o }$
which means that as the time progress, its amplitude will decrease.

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

In damped oscillatory motion a block of mass 400g is suspended to a spring of force constant 90 N/m in a medium and damping constant is 80g/s. Find time taken for its mechanical energy to drop to half of its initial value 

  1. 4.65 s

  2. 3.465 s

  3. 5 s

  4. 5.46 S
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mechanical energy E(t) = E0 * e^(-2bt), where b = c/(2m). Given m=0.4 kg, c=0.08 kg/s, b = 0.08 / (2 * 0.4) = 0.1 s^-1. We want E(t) = E0/2, so e^(-2 * 0.1 * t) = 0.5. -0.2t = ln(0.5) = -0.693. t = 0.693 / 0.2 = 3.465 s.