Physics

Oscillations and Simple Harmonic Motion

136 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

Two simple harmonic motions are represented by the equations 
$y _1=10\sin \left(3\pi t+\dfrac{\pi}{4}\right)$
and $y _2=5(3\sin 3\pi t+\sqrt 3 \cos 3\pi t)$ Their amplitudes are in the ratio of :

  1. $\sqrt 3$
  2. $1/\sqrt 3$
  3. $2$
  4. $1/6$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

y1 = 10 sin(3pi*t + pi/4), amplitude = 10. y2 = 5(3 sin(3pi*t) + sqrt(3) cos(3pi*t)). Using R = sqrt(A^2 + B^2 + 2AB cos(phi)), y2 = 5 * sqrt(3^2 + sqrt(3)^2) * sin(...) = 5 * sqrt(9+3) = 5 * sqrt(12) = 10 * sqrt(3). Ratio = 10 / (10 * sqrt(3)) = 1/sqrt(3).

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 audible, infra and ultra sound with its application study of sound physics

The direction of motion of a particle at any instant is given by

  1. Velocity

  2. Loudness

  3. Frequency

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

Velocity is a vector quantity defined as the rate of change of displacement with respect to time, which explicitly specifies both the speed and the direction of motion of a particle at any given instant.

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

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.

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 oscillating in simple harmonic motion is :

  1. Never in equilibrium because it is in motion

  2. Never in equilibrium because there is always a force

  3. In equilibrium at the ends of its path because of zero velocity there

  4. In equilibrium at the centre of its path because the acceleration is zero there
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In simple harmonic motion, a particle is in mechanical equilibrium at the center of its path because the restoring force and resulting acceleration are zero there, even though its velocity is at a maximum. At the extreme positions, the restoring force and acceleration are at their maximum values, so the particle is not in equilibrium.

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 block of mass $M$ is performing $SHM$ with amplitude $A$ on a smooth horizontal surface$.$ At the extreme position a small block of mass $m$ falls vertically and sticks to$M.$ then$,$ amplitude of oscillation will be                                               

  1. $A$
  2. $A\sqrt {\dfrac{M}{{M + m}}} $
  3. $A\left( {\dfrac{M}{{M + m}}} \right)$
  4. $A\left( {\dfrac{{M + m}}{m}} \right)$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 simple harmonic oscillator of angular frequency $2$ rad/s is acted upon by an external force $F = \sin t$ N. If the oscillator is at rest in its equilibrium position at $t= 0$, its position at later times is proportional to:

  1. $ \sin t + \cfrac{1}{2} \cos 2t$
  2. $ \cos t - \cfrac{1}{2} \sin 2t$
  3. $ \sin t + \cfrac{1}{2} \sin 2t$
  4. $ \sin t - \cfrac{1}{2} \sin 2t$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is a forced oscillation problem. The equation of motion is x'' + 4x = sin(t). The particular solution is of the form x = C*sin(t). Plugging in: -C*sin(t) + 4*C*sin(t) = sin(t) => 3C = 1 => C = 1/3. The general solution includes the homogeneous part A*sin(2t) + B*cos(2t). Matching initial conditions leads to the correct form.