Physics

Oscillations and Simple Harmonic Motion

138 Questions

Oscillations and simple harmonic motion focus on amplitude, damped vibrations, and force equations. These physics principles are essential for various engineering and civil services examinations. Review these problems to understand the core mechanics of oscillating bodies.

Damped harmonic oscillationSHM amplitudeForce equationsForced oscillationVibratory motion concepts

Oscillations and Simple Harmonic Motion Questions

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

Vibrations of period 0.25 s propagate along a straight line at a velocity of 48 cm/s. One second after the emergence of vibrations at the initial point, displacement of the point, 47 cm from it is found to be 3 cm. Then,

  1. amplitude of vibrations is 6 cm.
  2. amplitude of vibrations is $3 \sqrt{2} cm.$

  3. amplitude of vibrations is 3 cm.

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

The wavelength of the wave can be found by using $\dfrac{\lambda}{T}=v$

$\implies \lambda=vT=48cm/s\times 0.25s=12cm$
Four full wavelengths complete at a distance of 48cm.
Thus a point 47cm lag by a phase difference of $\dfrac{2\pi}{\lambda}(48cm-47cm)=\dfrac{\pi}{6}$
Let the amplitude of vibrations be $A$.
Thus the displacement at the given point=$Asin(\dfrac{\pi}{6})=\dfrac{A}{2}=3cm$
$\implies A=6cm$
Thus correct answer is option A.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

The displacement of an elastic wave is given by the function $y= 3\ sin \omega t+4\ cos\omega t$, where $y$ is in $cm$ and $t$ is in $s$. The resultant amplitude is 

  1. $3 cm$
  2. $ 4 cm$
  3. $ 5 cm$
  4. $7 cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here, we have given: $y=3sin\omega t+4cos\omega t$


So, two components are there, $3sin\omega t $ and $4cos\omega t$


where, individual amplitudes are given by
$A _1= 3 cms$ and $A _2=4 cms .$

so , resultant amplitude will be, 
$A=\sqrt{A _1^2 +A _2^2}=\sqrt{3^2+4^2}$

$A=5 cms$


Multiple choice physics structure of earth seismic waves and tsunami causes of earthquakes origin of earth and its internal energy transfer of charge lightning safety

The amplitude of vibrations measured on the Richter's scale increase by steps of about

  1. 10

  2. 20

  3. 30

  4. 40
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Answer is A.

The amplitude of vibrations measured on the Richter's scale increase by steps of about 10.
The Richter magnitude scale was developed in 1935 by Charles F. Richter of the California Institute of Technology as a mathematical device to compare the size of earthquakes. The magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs. Adjustments are included in the magnitude formula to compensate for the variation in the distance between the various seismographs and the epicenter of the earthquakes. On the Richter Scale, magnitude is expressed in whole numbers and decimal fractions. For example, a magnitude of 5.3 might be computed for a moderate earthquake, and a strong earthquake might be rated as magnitude 6.3. Because of the logarithmic basis of the scale, each whole number increase in magnitude represents a tenfold increase in measured amplitude; as an estimate of energy, each whole number step in the magnitude scale corresponds to the release of about 31 times more energy than the amount associated with the preceding whole number value.

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 number of cycles an oscillator completes in each second is called its _______________.

  1. Frequency

  2. Velocity

  3. Amplitude

  4. Angular velocity
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The number of cycles an oscillator completes in each second is called its frequency.
The frequency (f) of a wave is the number of full wave forms generated per second. This is the same as the number of repetitions per second or the number of oscillations per second.  

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

Frequency of vibration of a particle is 10 Hz. If the amplitude of vibration is doubled, what will be the change in frequency of vibration

  1. frequency doubles

  2. frequency becomes halved

  3. frequency remains same

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

Frequency is a characteristic of source and does not change with amplitude of the wave

The correct option is (c)

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 time period of a system executing wave motion depends upon

  1. elasticity

  2. inertia

  3. Amplitude

  4. restoring force
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Time period of oscillations is directly proportional to square root of modulus of elasticity and inversely proportional to density. Thus option (a) is the correct option

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 vibrates 10 times in 1 sec. What is the time period of vibration of the particle

  1. 10 Sec

  2. 1 Sec

  3. 0.1 Sec

  4. 0.01 sec
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Time period of vibration is time taken for 1 vibration

Thus 10 vibrations are completed in 1 sec or 1 vibration will taken only 1/10=0.1 sec

The correct option is (c)

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 equation of motion of a particle is $x = a cos(\alpha t)^2$. The motion is

  1. periodic but not oscillatory

  2. periodic and oscillatory

  3. oscillatory but not periodic

  4. neither periodic nor oscillatory.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The motion is oscillatory but not periodic because the oscillations are followed from the maximum displacement (negative extreme) at t=0, the corresponding echo is equal to π/2

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

In the equations below, A, B, $\omega$ and $\phi$ are constants; $y$ and $t$ are variables; $t$ represents time. Only one of the following equations does not represent SHM. Which one is that?

  1. $y= A sin \omega t$
  2. $y= B cos \omega t$
  3. $y= A sin \omega t + B cos \omega t$
  4. $y= A sin \omega t + B cos (2\omega t)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A linear combination of coherent simple harmonic motions would result in another simple harmonic motion.

But the combination of two incoherent simple harmonic motions($Asin\omega t,B cos(2\omega t)$) is NOT an SHM.
Hence the answer is option D.

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

Uniform circular motion can also be represented by a simple harmonic oscillator.
State whether given statement is True/False?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The above statement is true as we can represent uniform circular motion by simple harmonic oscillator.

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

In periodic motion, the displacement is

  1. directly proportional to the restoring force

  2. inversely proportional to the restoring force

  3. independent of restoring force

  4. independent of any force acting on the particle
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The displacement of the body from its equilibrium is directly proportional to the restoring force. Therefore, higher the displacement, higher is the restoring force.

The correct option is (a)

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 thin spherical shell of mass $M$ and radius $R$ has a small hole. A particle of mass $m$ is released at its mouth. Then

  1. the particle will execute SHM inside the shell

  2. the particle will oscillate inside the shell, but the oscillations are not simple harmonic

  3. the particle will not oscillate, but the speed of the particle will go on increasing

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

Firstly ,given that it is a  thin shell i.e hollow sphere then it will perform oscillation on SHM.

In case of solid sphere it performs SHM.