Tag: oscillatory and periodic motion

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Questions Related to oscillatory and periodic motion

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

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

  1. Periodic

  2. Oscillatory

  3. $SHM$

  4. Both (1) & (2)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The equation x = 2*sin(wt) + 3*sin^2(wt) can be written as 2*sin(wt) + 1.5*(1 - cos(2wt)). This is a sum of two periodic functions with different frequencies, so the motion is periodic and oscillatory, but not SHM because it is not a single sine/cosine term.

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

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 

  1. $0.6 m$

  2. $0.2 m$

  3. $0.4 m$

  4. $0.1 m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

Which of the following equation does not represent a simple harmonic motion:

  1. $y=a\sin\omega t$

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

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

  4. $y= a\tan\omega t$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

SHM requires a restoring force proportional to displacement, resulting in a sine or cosine function of time. Tangent functions do not represent SHM.

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

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

  1. more than three

  2. 3

  3. 2

  4. 1
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. amplitude, frequency and initial phase.

  2. amplitude, frequency and wavelength

  3. frequency and wavelength.

  4. frequency, wavelength and initial phase.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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?

  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.
Reveal answer Fill a bubble to check yourself
B Correct answer
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.