Tag: oscillatory and periodic motion

Questions Related to oscillatory and periodic motion

The motion represented by equation $x=2\sin \omega t+3\sin^{2}\omega t$ 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. Periodic

  2. Oscillatory

  3. $SHM$

  4. Both (1) & (2)

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Correct Option: B

A particle of mass $0.1 kg$ executes SHM under a force $F = (-10 x) N$. Speed of particle at mean position is $6 m/s$. Then amplitude of oscillations 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. $0.6 m$

  2. $0.2 m$

  3. $0.4 m$

  4. $0.1 m$

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Correct Option: A
Explanation:

$\begin{array}{l} M=0.1\, Kg \ f=-10x \ \Rightarrow k=10 \ w=\sqrt { \frac { k }{ m }  }  \ =\sqrt { \frac { { 10 } }{ { 0.1 } }  } =10 \ { V _{ \max   } }=6m/s \ \Rightarrow A=\frac { 6 }{ { 10 } } =0.6m \ Hence,\, the\, option\, A\, is\, the\, correct\, answer. \end{array}$

Select the correct statements.

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. A simple harmonic motion is necessarily periodic.

  2. A simple harmonic motion is necessarily oscillatory.

  3. An oscillatory motion is necessarily periodic.

  4. A periodic motion is necessarily oscillatory.

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Correct Option: A,B,D

Equation of SHM is $x=10\sin{10\pi t}$. Find the distance between the two points where speed is $50\pi$ $cm/sec$. $x$ is in cm and $t$ is in seconds

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. $10cm$

  2. $20cm$

  3. $17.32cm$

  4. $8.66cm$

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Correct Option: D

Which of the following equation does not represent a simple harmonic 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. $y=a\sin\omega t$

  2. $y=b\cos\omega t$

  3. $y=a\sin\omega t+b\cos\omega t$

  4. $y= a\tan\omega t$

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Correct Option: D

What is the number of degrees of freedom of an oscillating simple pendulum?

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. more than three

  2. 3

  3. 2

  4. 1

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Correct Option: C
Explanation:

There are 2 degrees of freedom, 1 translational along which the pendulum bob moves, and second rotational - the hinge about which it forms an arc motion.

All oscillatory motions are ______

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. periodic

  2. linear

  3. rotatory

  4. curvilinear

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Correct Option: A
Explanation:

All oscillatory is periodic, as in all oscillatory motion particle repeats its position after a certain interval of time.

State whether true or false.
The needle of a moving sewing machine executes 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. True

  2. False

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Correct Option: A
Explanation:

The needle of swing machine has a to and fro motion about mea position. So, its a oscillatory motion.

Simple harmonic oscillation of a given system can be specified completely by stating its: 

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. amplitude, frequency and initial phase.

  2. amplitude, frequency and wavelength

  3. frequency and wavelength.

  4. frequency, wavelength and initial phase.

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Correct Option: A
Explanation:

Although waves consist of oscillation, there is no wavelength in a pure oscillation. It is there only in waves. 

Simple harmonic motion (SHM) is a technical term used to describe a certain kind of idealized oscillation. Practically all the oscillations that one can see directly in the natural world are much more complicated than SHM. Why then do physicists make such a big deal out of studying SHM?

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 is the only kind of oscillation that can be described mathematically

  2. Any real oscillation can be analysed as a superposition (sum or integral) of SHMs with different frequencies

  3. Physics is concerned mainly with the unnatural world.

  4. Students are too stupid to appreciate the real world.

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Correct Option: B
Explanation:

Simple harmonic motion provides a basis for the characterization of more complicated motions through the techniques of Fourier analysis. Here any waveform can be represented as closely as desired by the combination of a sufficiently large number of sinusoidal waves that form a harmonic series.   Fourier's theorem suggests that any periodic function can be represented as an algebraic sum of sine and cosine functions called a Fourier Series.