Tag: oscillations

Questions Related to oscillations

The net external force acting on the disc when its centre of mass is at displacement $x$ with respect to its equilibrium position is:

force in shm oscillations oscillation and waves physics

  1. $-kx$

  2. $-2kx$

  3. $-\dfrac{2kx}{3}$

  4. $\dfrac{4kx}{3}$

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Correct Option: D

A particle is in S.H.M of amplitude $ 2$ cm. At extreme position the force is $4$N. At the point mid-way between mean and extreme position, the force is :

force in shm oscillations oscillation and waves physics

  1. $1$ N

  2. $2$N

  3. $3$N

  4. $4$N

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Correct Option: B
Explanation:

Amplitude = 2 cm
Force = 4N
$F = mw^{2}A=4$
$F _{1} = mw^{2}x$

Since $F$ is directly proportional to $x$ so , at midpoint the force when the amplitude is $2 \ cm$ will be $2N$

A 1 kg mass executes SHM with an amplitude 10 cm, it takes $2\pi$ seconds to go from one end to the other end. The magnitude of the force acting on it at any end is :

force in shm oscillations oscillation and waves physics

  1. 0.1 N

  2. 0.2 N

  3. 0.5 N

  4. 0.05 N

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Correct Option: A
Explanation:

As $  w  = \cfrac{2\pi}{T} = 1 \ rad/sec $ ;    Amplitude  $A  = 0.1 m$
magnitude of  force $ = m \times w^{2}.A$
                                  $=  0.1 N$

An elastic ball of density $d$ is released and it falls through a height $h$ before striking the surface of liquid of density $\rho(d < \rho)$. The motion of ball is:

force in shm oscillations oscillation and waves physics

  1. Periodic

  2. S.H.M.

  3. Circular

  4. Parabolic

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Correct Option: A

A body of mass 1/4 kg is in S.H.M and its displacement is given by the relation $y= 0.05 sin(20t+\dfrac{\pi }{2})$ m. If $t$ is in seconds, the maximum force acting on the particle is:

force in shm oscillations oscillation and waves physics

  1. $5$ N

  2. $2.5$ N

  3. $10$ N

  4. $0.25$ N

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Correct Option: A
Explanation:

$F= m\omega^{2}A$
$\omega = 20   rad / sec$
$A =   0.05   m$
Thus
$F= \dfrac{1}{4}\times 20\times 20\times \dfrac{1}{20}$
$=5 N $

A resonance tube is resonated with tuning fork of frequency 256 Hz. If the length of first and second resonating air columns are 32 cm and 100 cm, then end correction will be 

resonance oscillations physics

  1. $1 cm$

  2. $2 cm$

  3. $4 cm$

  4. $6 cm$

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Correct Option: B

If $\omega _{0}$ is natural frequency of damped forced oscillation and $p$ that of driving force, then for amplitude resonance

resonance oscillations physics

  1. $p _{r}= \omega _{0}$

  2. $p _{r}< \omega _{0}$

  3. $p _{r}> \omega _{0}$

  4. $p _{r}> = \omega _{0}$

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Correct Option: A

Which of the following is an example of mechanical resonance?

resonance oscillations physics

  1. A child on a swing.

  2. A pendulum.

  3. A tuning fork.

  4. Nuclear magnetic resonance

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Correct Option: A,B
Explanation:

$Answer:-$ A,B

Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings and airplanes—a phenomenon known as resonance disaster.

Various examples of mechanical resonance include:-

  • Most clocls keep time by mechanical resonance in a balance wheel, pendulum, or quartz crystal.
  • The resonance of the basilar membranein the ear.
  • Making a child's swing swing higher by pushing it at each swing.
  • A wineglass breaking when someone sings a loud note at exactly the right pitch.

 A mechanical system is oscillating at resonance with a constant amplitude. Which one of the following statements is not correct?

resonance oscillations physics

  1. The applied force prevents the amplitude from becoming too large.

  2. The frequency of the applied force is the same as the natural frequency of oscillation of the system.

  3. The total energy of the system is constant.

  4. The amplitude of oscillations depends on the amount of damping.

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Correct Option: A
Explanation:

The applied force prevents the amplitude from becoming too large.


Option A is correct.

Which of the following is an example of acoustic resonance?

resonance oscillations physics

  1. Feedback in guitars

  2. A pendulum

  3. Nuclear magnetic resonance

  4. A swing

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Correct Option: A
Explanation:

$Answer:-$ A

Acoustic resonance is a phenomenon that consists of a given acoustic system amplifying a sound whose frequency matches one of its own natural frequencies of vibration (its resonance frequencies).
The resonance of a tube of air is related to the length of the tube, its shape, and whether it has closed or open ends. Musically useful tube shapes are conical and cylindrical . A pipe that is closed at one end is said to be stopped while an open pipe is open at both ends. Modern orchestral flutes behave as open cylindrical pipes; clarinets and lip-reed instruments (brass instruments) behave as closed cylindrical pipes; and saxophones, bassoons as closed conical pipes. Vibrating air columns also have resonances at harmonics, like strings (in guitars).