Tag: oscillatory and periodic motion

Questions Related to oscillatory and periodic motion

Which of the following conditions must be satisfied for a body to oscillate or vibrate?
A: The body must have inertia to keep it moving across the mid point of its path.
B: There must be a restoring force to accelerate the body towards the midpoint.
C: The fractional force acting on the body against its motion must be small.

physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

  1. Only A

  2. Only A and B

  3. Only B and C

  4. All A, B and C

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Correct Option: D

An object swinging on the end of a string forms a simple pendulum. Some students (and some texts) often cite the simple pendulum's motion as an example of SHM. That is not quite accurate because the motion is really

physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

  1. approximately SHM only for small amplitudes

  2. exactly SHM only for amplitudes that are smaller than a certain value

  3. approximately SHM for all amplitudes.

  4. None of the above

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Correct Option: A
Explanation:

An object performing SHM moves along a straight path.

For large amplitudes, a pendulum moves in a curved path.

Which of  the  following regarding oscillatory motion is true?

physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

  1. Motion of the earth is periodic but not oscillatory because it is not to and fro.

  2. Quivering of the string of the musical instrument is an example of oscillatory motion

  3. Motion of the earth is periodic and oscillatory motion because it is not to and fro.

  4. None of the above

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Correct Option: A
Explanation:

Oscillator motion is to and fro motion about a mean position. Earth motion is not a to and fro motion here, hence it is not an oscillatory motion. But as earth motion is repeated in a regular interval of time, its motion is periodic.

Which of the following is an example of oscillatory motion? 

physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

  1. Heart beat of a persion

  2. Motion of earth around the sun

  3. Motion of Hally's comet around the sun

  4. Oscillations of a simple pendulam

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Correct Option: D
Explanation:

Oscillation of a simple pendulum is a simple harmonic motion.

The displacement of a particle is represented by the equation $y=sin^3(\omega t)$. The motion is 

physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

  1. non-periodic

  2. periodic but not simple harmonic

  3. simple harmonic with period $\dfrac{2 \pi}{\omega}$

  4. simple harmonic with period $\dfrac{\pi}{\omega}$

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Correct Option: B
Explanation:

Given the equation of displacement of the particle, $y={ sin }^{ 3 }\omega t$

We know $sin3\theta =3sin\theta -4{ sin }^{ 3 }\theta $
Hence, $y=\frac { (3sin\omega t-4sin3\omega t) }{ 4 } \ \Rightarrow 4\frac { dy }{ dt } =3\omega cos\omega t-4\times [3\omega cos3\omega t]\ \Rightarrow 4\times \frac { { d }^{ 2 }y }{ { dt }^{ 2 } } =-3{ \omega  }^{ 2 }sin\omega t+12\omega sin3\omega t\ \Rightarrow \frac { { d }^{ 2 }y }{ { dt }^{ 2 } } =\frac { -3{ \omega  }^{ 2 }sin\omega t+12\omega sin3\omega t }{ 4 } \ \Rightarrow \frac { { d }^{ 2 }y }{ { dt }^{ 2 } } $ is not proportional to y. 
Hence, the motion is not SHM. 
As the expression is involving sine function, hence it will be periodic. 
Also ${ sin }^{ 3 }\omega t={ \left( sin\omega t \right)  }^{ 3 }\ ={ [sin(\omega t+2\pi )] }^{ 3 }\ ={ [sin(\omega t+2\pi /\omega )] }^{ 3 }$
Hence, $y={ sin }^{ 3 }\omega t$ represents a periodic motion with period $2\pi /\omega $.

A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of 40 cm. The block just loses contact with the plank when the later is momentarily at rest. Then

physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

  1. the period of oscillation is $2\pi /5\ s$

  2. the block weighs double its weight when the plank is at one of the positions of momentary at rest

  3. the block weighs 1.5 times its weight on the plank half way down

  4. the block weighs its true weight on the plank, when the latter moves fast

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Correct Option: B

In an electronic watch, the component corresponding to the pendulum of a pendulum clock is a__?

physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

  1. Diode

  2. Transistor

  3. Crystal oscillator

  4. Balance wheel

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Correct Option: C

An oscillator is producing FM waves of frequency 2kHz with avariation of 10kHz. The modulating index=?

physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

  1. 0.20

  2. 5.0

  3. 0.67

  4. 1.5

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Correct Option: B
Explanation:

Modulation Index , $m _f=\dfrac{\text{Maximum frequency deviation}}{\text{Modulating frequency}}$

$\Rightarrow m _f= \dfrac{10 kHz}{2 kHz}$
$\Rightarrow m _f=5$

Which one of the following will take place when a watch based on oscillating spring is taken to a deep mine?

physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

  1. It will indicate the same time  on earth

  2. It will become fast

  3. It will become slow

  4. It will stop working

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Correct Option: A

A simple harmonic oscillator of angular frequency 2 rad $s^{-1}$ is acted upon by an external force $F= sin tN.$ If the oscillator is at rest in its equilibrium position at t=0, its position at later times is proportional to 

physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

  1. $ sin t+ \frac{1}{2}cos 2t$

  2. $ cos t -\frac{1}{2}sin2t$

  3. $sint -\frac{1}{2}sin2t$

  4. $sin t +\frac{1}{2}sin 2t$

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Correct Option: C
Explanation:

The solution contains term proportional to $sin t$, $sin 2t$ & the only option consistent with initial conditions is (C)