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## Oscillations Class 11 MCQs Questions with Answers

Multiple Choice Type Questions

Question 1.

In S.H.M, the vibration of which of the following is not a sine curve?

(a) Timeperiod

(b) Velocity

(c) Displacement

(d) Acceleration

## Answer

Answer: (a) Timeperiod

Question 2.

Which of the following is not essential for S.H.M.?

(a) Gravity

(b) Restoring force

(c) Inertia

(d) Material medium

## Answer

Answer: (a) Gravity

Question 3.

Damping in oscillatory motion is caused by

(a) Friction

(b) Restoring force

(c) Both restoring force and friction

(d) Neither friction nor restoring force

## Answer

Answer: (a) Friction

Question 4.

What determines the frequency of natural oscillations of the system?

(a) Elasticity alone

(b) Inertia alone

(c) Both elasticity and inertia

(d) Neither elasticity nor inertia

## Answer

Answer: (c) Both elasticity and inertia

Question 5.

Which of the following quantities connected with S.H.M. do not vary periodically?

(a) Displacement

(b) Velocity

(c) Acceleration

(d) Total energy

## Answer

Answer: (d) Total energy

Question 6.

Which of the following characteristics does not change due to the damping of S.H.M.?

(a) Amplitude

(b) Time period

(c) Angular frequency

(d) Initial phase

## Answer

Answer: (d) Initial phase

Question 7.

The restoring force acting on the particle executing S.H.M. is

(a) directly proportional to displacement.

(b) inversely proportional to displacement.

(c) directed in the same direction as the displacement.

(d) independent of displacement.

## Answer

Answer: (a) directly proportional to displacement.

Question 8.

In S.H.M., the particle is

(a) always accelerated

(b) always retarded.

(c) neither accelerated nor retarded.

(d) accelerated and retarded alternately.

## Answer

Answer: (d) accelerated and retarded alternately.

Question 9.

Which of the following is not the characteristic of S.H.M.?

(a) Periodic nature.

(b) Displacement time graph is a sine curve.

(c) Acceleration is zero at mean position.

(d) Projection of a uniform circular motion on any straight line.

## Answer

Answer: (d) Projection of a uniform circular motion on any straight line.

Question 10.

The amplitudes of two similar pendulums are 2 cm and 5 cm. The ratio of their energies is

(a) 2 : 5

(b) 5 : 2

(c) 4 : 25

(d) None of the above

## Answer

Answer: (c) 4 : 25

Question 11.

The amplitude of a simple harmonic oscillator is doubled, then

(a) its energy is doubled.

(b) maximum velocity is doubled.

(c) time period is doubled.

(d) time period remains same.

## Answer

Answer: (d) time period remains same.

Question 12.

The force constant of a simple pendulum is

(a) directly proportional to the length of the pendulum.

(b) directly proportional to the mass of the bob.

(c) inversely proportional to both the mass of the bob and the length of the pendulum.

(d) independent of the mass of the bob as well as length of the pendulum.

## Answer

Answer: (b) directly proportional to the mass of the bob.

Question 13.

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

(a) One

(b) Two

(c) Three

(d) More than three

## Answer

Answer: (b) Two

Question 14.

An object is performing a uniform circular motion. Its motion is:

(a) periodic and simple harmonic.

(b) periodic but not simple harmonic.

(c) a periodic.

(d) none of the above.

## Answer

Answer: (a) periodic and simple harmonic.

Question 15.

A ball is dropped in a tunnel dug along the diameter of earth. When it is at the centre of earth, then it has

(a) mass

(b) acceleration

(c) weight

(d) kinetic energy

## Answer

Answer: (a) and (d).

Question 16.

It is required to double the frequency of a simple harmonic oscillator. It can be done by

(a) increasing the mass to four times its original value.

(b) reducing the mass to \(\frac {1}{4}\) th of its original value.

(c) reducing the mass to \(\frac {1}{2}\) of its original value.

(d) doubling the mass.

## Answer

Answer: (b) reducing the mass to \(\frac {1}{4}\) th of its original value.

Question 17.

The total energy of a particle executing S.H.M. is proportional to:

(a) frequency of oscillation.

(b) square of the amplitude.

(c) velocity in mean position.

(d) displacement from the mean position.

## Answer

Answer: (b) square of the amplitude.

Question 18.

A simple pendulum has time period T on the surface of earth. When it is taken to a height h, then its time period will be

(a) constant

(b) more than T

(c) less than

(d) None of the above

## Answer

Answer: (b) more than T

Question 19.

A uniform spring of force constant k is cut into two equal parts. Then each half has a force constant equal to

(a) k

(b) \(\frac {k}{2}\)

(c) 2k

(d) 4k

## Answer

Answer: (c) 2k

Question 20.

To identical springs each of spring constant k are connected in series. The resultant spring constant is

(a) k

(b) 2k

(c) 4k

(d) \(\frac {k}{2}\)

## Answer

Answer: (d) \(\frac {k}{2}\)

Question 21.

To identical springs each of spring constant k are connected in parallel. The resultant spring constant is

(a) kt

(a) 2k

(c) 4k

(d) 4k

## Answer

Answer: (a) kt

Question 22.

A pendulum clock is in a lift falling freely. Then

(a) it runs slower.

(b) it runs faster.

(c) it keeps correct time.

(d) no oscillations occur and the clock does not operate at all.

## Answer

Answer: (d) no oscillations occur and the clock does not operate at all.

Question 23.

The oscillations of a body are damped because of:

(a) density of the body.

(b) weight of the body.

(c) elasticity of the body.

(d) frictional forces offered by the surrounding medium.

## Answer

Answer: (d) frictional forces offered by the surrounding medium.

Question 24.

Resonant vibrations are a special case of:

(a) free vibrations

(b) natural vibrations

(c) forced vibrations

(d) damped vibrations

## Answer

Answer: (c) forced vibrations

Question 25.

The energy of the particle executing damped oscillations decreases with time, because work is done against:

(a) restoring force.

(b) elastic tension.

(c) frictional force.

(d) both restoring force and friction.

## Answer

Answer: (c) frictional force.

Fill in the blanks

Question 1.

The magnitude of acceleration of a particle in S.H.M. is the ………………… at the end points, (least, greatest)

## Answer

Answer: greatest

Question 2.

A particle in S.H.M. has ………………… speed and ………………… magnitude of acceleration at its mean position, (maximum, minimum)

## Answer

Answer: maximum, minimum

Question 3.

For a particle in S.H.M. with a given mass m and force constant k, quantities which depend on initial conditions are ………………… (time period, amplitude, phase, total energy, frequency)

## Answer

Answer: amplitude, phase and total energy

Question 4.

The time period of a particle in S.H.M. depends in general on ………………… but is independent of ………………… (amplitude, force constant, initial phase, ma&s, total energy)

## Answer

Answer: mass, force constant; amplitude, initial phase, total energy

Question 5.

The restoring force in S.H.M. is ………………… in magnitude when the particle is instantaneously at rest, (zero, maximum)

## Answer

Answer: maximum

Question 6.

The total energy of a particle in S.H.M. is equal to the ………………… at the extreme positions and the ………………… at the mean position. (K.E, P.E.)

## Answer

Answer: P.E, K.E.

Question 7.

The acceleration curve of a particle executing S.H.M. leads its displacement curve by …………………

## Answer

Answer: π

Question 8.

The distance covered by a particle in S.H.M. in one time period is …………………

## Answer

Answer: 4r (where r is the amplitude).

Question 9.

……………….. is the phase difference between the displacement and the velocity of a particle in S.H.M.

## Answer

Answer: \(\frac {π}{2}\)

Question 10.

The acceleration of a particle in S.H.M. is ………………… when its velocity is maximum.

## Answer

Answer: zero.

Question 11.

………………… and ………………… quantities are always negative in S.H.M.

## Answer

Answer: \(\vec{a}\).\(\vec{r}\) and \(\vec{F}\).\(\vec{r}\)

Question 12.

………………… quantity is always positive in S.H.M.

## Answer

Answer: \(\vec{F}\).\(\vec{a}\)

Question 13.

…………………, ……………….., ………………… and ………………… are always zero in S.H.M.

## Answer

Answer: \(\vec{F}\)×\(\vec{a}\), \(\vec{F}\)×\(\vec{r}\). \(\vec{v}\)×\(\vec{r}\), \(\vec{a}\)×\(\vec{r}\).

Question 14.

Time period of a simple pendulum will be double if we …………………

## Answer

Answer: increase the length 4 times.

Question 15.

A particle performing S.H.M. passing through mean position has …………………

## Answer

Answer: maximum kinetic energy.

True/False Type Questions

1. Mark the True/False statements out of the following

(a) Proportionality between restoring force and displacement from equilibrium position is a necessary and sufficient condition for S.H.M.

(b) Motion of a particle performing a uniform circular motion is periodic and but not S.H.M.

(c) All oscillatory motions are periodic but all periodic motions are not oscillatory.

## Answer

Answer:

(a) True

(b) True

(c) True

2. Select True/False statements out of the following

(a) Velocity of a particle in S.H.M. is maximum (v = rω) at mean position.

(b) Acceleration of a particle in S.H.M. is maximum at mean position.

(c) Time period of a simple pendulum is independent of amplitude of vibration so long as the angle of oscillation is small.

## Answer

Answer:

(a) True

(b) False

(c) True.

3. Select True/False statements out of the following

(a) A second’s pendulum has a time period of two seconds.

(b) Time period of motion of liquid column in a U-tube is

(i) independent of density of liquid,

(ii) independent of area of cross-section of the tube.

## Answer

Answer:

(a) True

(b) (i) True

(ii) True.

4. Select True/False statements out of the following :

(a) In free oscillations, a body vibrates with its natural frequency.

(b) In undamped free oscillations, the amplitude of the oscillations remain constant.

## Answer

Answer:

(a) True

(b) True

5. Select True/False statements out of the following

(a) In forced oscillations, a body oscillates under the effect of an external periodic force of frequency other than its natural frequency.

(b) In resonant oscillations, the frequency of the periodic force is always equal to natural frequency of oscillation of the object.

## Answer

Answer:

(a) True

(b) True

6. Select True/False statements out of the following

(a) Motion of a satellite around a planet is periodic.

(b) For S.H.M., the motion has to be periodic and oscillatory.

## Answer

Answer:

(a) True

(b) True

7. Select True/False statements out of the following :

(a) The displacement curve of a particle in S.H.M. lags behind its velocity curve by \(\frac {π}{2}\).

(b) The motion of the bob of a simple pendulum is periodic and oscillatory.

## Answer

Answer:

a) True

(b) True

8. Select True/False statements out of the following

(a) The elastic potential energy of a spring balance is maximum at either of its extreme positions.

(b) When a particle executes S.H.M. then its K.E. does not remain constant throughout its vibration.

## Answer

Answer:

(a) True

(b) True

9. Select True/False statements out of the following

(a) When the displacement of a particle in S.H.M. is maximum, its velocity is also maximum.

(b) When the displacement of a particle in S.H.M. is maximum, its acceleration is maximum.

## Answer

Answer:

(a) False

(b) True

Match Type Questions

Column I | Column II |

(a) Maximum velocity (rω) in S.H.M. | (i) extreme positions |

(b) Minimum (zero) velocity in S.H.M. | (ii) mean position |

## Answer

Answer:

Column I | Column II |

(a) Maximum velocity (rω) in S.H.M. | (ii) mean position |

(b) Minimum (zero) velocity in S.H.M. | (i) extreme positions |

Column I | Column II |

(a) Acceleration of S.H.M. is zero | (i) extreme positions |

(b) Acceleration of S.H.M. is maximum (i.e. a = -ω²r) | (ii) mean position |

## Answer

Answer:

Column I | Column II |

(a) Acceleration of S.H.M. is zero | (ii) mean position |

(b) Acceleration of S.H.M. is maximum (i.e. a = -ω²r) | (i) extreme positions |

Column I | Column II |

(a) Total energy in S.H.M. is equal to K.E. | (i) extreme positions |

(b) Total energy in S.H.M. is equal to P.E. | (ii) mean position |

## Answer

Answer:

Column I | Column II |

(a) Total energy in S.H.M. is equal to K.E. | (ii) mean position |

(b) Total energy in S.H.M. is equal to P.E. | (i) extreme positions |

Column I | Column II |

(a) K.E. in any position in S.H.M. | (i) \(\frac {1}{2}\) mω²y² |

(b) P.E. in any position in S.H.M. | (ii) \(\frac {1}{2}\) mω²(r² – y²) |

(c) Total energy in any position | (iii) \(\frac {1}{2}\) mω²r² |

## Answer

Answer:

Column I | Column II |

(a) K.E. in any position in S.H.M. | (ii) \(\frac {1}{2}\) mω²(r² – y²) |

(b) P.E. in any position in S.H.M. | (i) \(\frac {1}{2}\) mω²y² |

(c) Total energy in any position | (iii) \(\frac {1}{2}\) mω²r² |

Column I | Column II |

(a) A body vibrates with its natural frequency | (i) forced oscillations |

(b) A body vibrates with a frequency other than its natural frequency under the effect of a periodic force | (ii) resonant oscillations |

(c) When the frequency of the external periodic force is equal to the natural frequency of the body | (iii) free oscillations |

## Answer

Answer:

Column I | Column II |

(a) A body vibrates with its natural frequency | (iii) free oscillations |

(b) A body vibrates with a frequency other than its natural frequency under the effect of a periodic force | (i) forced oscillations |

(c) When the frequency of the external periodic force is equal to the natural frequency of the body | (ii) resonant oscillations |

Column I | Column II |

(a) A particle executing S.H.M. | (i) acceleration of constant magnitude and direction |

(b) A body falling under the gravity near the surface of the earth | (ii) acceleration of constant magnitude and changing direction |

(c) A body falling under from a height comparable to the radius of Earth | (iii) acceleration of changing magnitude but constant direction |

(d) A stone revolving in a circle with constant speed | (iv) acceleration of changing magnitude and direction |

## Answer

Answer:

Column I | Column II |

(a) A particle executing S.H.M. | (iv) acceleration of changing magnitude and direction |

(b) A body falling under the gravity near the surface of the earth | (i) acceleration of constant magnitude and direction |

(c) A body falling under from a height comparable to the radius of Earth | (iii) acceleration of changing magnitude but constant direction |

(d) A stone revolving in a circle with constant speed | (ii) acceleration of constant magnitude and changing direction |

Column I | Column II |

(a) In S.H.M the variation is not a sine or consine curve | (i) velocity, acceleration or displacement |

(b) In S.H.M the variation is a sine or a cosine curve | (ii) time period |

(c) In S.H.M its variation is not periodic but it is constant and is represented by a straight line parallel to the displacement axis | (iii) total energy |

## Answer

Answer:

Column I | Column II |

(a) In S.H.M the variation is not a sine or consine curve | (ii) time period |

(b) In S.H.M the variation is a sine or a cosine curve | (i) velocity, acceleration or displacement |

(c) In S.H.M its variation is not periodic but it is constant and is represented by a straight line parallel to the displacement axis | (iii) total energy |

Column I | Column II |

(a) The graph between the length of a simple pendulum and its time period will be | (i) T |

(b) If the length of seconds pendulum on earth is about lm, then its length on the moon will be | (ii) Parabola |

(c) Two pendulums oscillate with a constant phase difference of 90°. If the, time period of one is T, then that of the other will be | (iii) \(\frac {1}{6}\) m |

## Answer

Answer:

Column I | Column II |

(a) The graph between the length of a simple pendulum and its time period will be | (ii) Parabola |

(b) If the length of seconds pendulum on earth is about lm, then its length on the moon will be | (iii) \(\frac {1}{6}\) m |

(c) Two pendulums oscillate with a constant phase difference of 90°. If the, time period of one is T, then that of the other will be | (i) T |

Column I | Column II |

(a) Causes damping in oscillatory motion | (i) initial phase |

(b) It does not change in damped S.H.M. | (ii) displacement |

(c) Restoring force acting on particles executing undamped natural oscillations is directly proportional to | (iii) friction |

## Answer

Answer:

Column I | Column II |

(a) Causes damping in oscillatory motion | (iii) friction |

(b) It does not change in damped S.H.M. | (i) initial phase |

(c) Restoring force acting on particles executing undamped natural oscillations is directly proportional to | (ii) displacement |

Column I | Column II |

(a) If two springs each having spring constant k are connected in series, then the resultant spring constant is | (i) 2k |

(b) If two springs each having spring constant k are connected in parallel, then the resultant spring constant is | (ii) \(\frac {k}{2}\) |

(c) A uniform spring having spring or force constant k, is cut into two equal halves, then force constant of each half is | (iii) 2k |

## Answer

Answer:

Column I | Column II |

(a) If two springs each having spring constant k are connected in series, then the resultant spring constant is | (ii) \(\frac {k}{2}\) |

(b) If two springs each having spring constant k are connected in parallel, then the resultant spring constant is | (iii) 2k |

(c) A uniform spring having spring or force constant k, is cut into two equal halves, then force constant of each half is | (i) 2k |

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