NCERT Solutions for class 11 Physics | Chapter 14 - Oscillations

(1) A particle is in linear simple harmonic motion between two points A and B, 10 cm apart. Taken the direction from A to B as the +ve direction and choose the correct statements.

[A] the sign of velocity, acceleration, and force on the particle when it is 3 cm away from A going towards B are positive
[B] the sign of velocity of the particle at C going towards O is negative
[C] the sign of velocity, acceleration, and force on the particle when it is 4 cm away from B going towards A are negative
[D] the sign of acceleration and force on the particle when it is at point B is negative
Answer: A, C, D
(2) A body is performing SHM. Then its
[A] average total energy per cycle is equal to its maximum kinetic energy
[B] average kinetic energy per cycle is equal to half of its maximum kinetic energy
[C] mean velocity over a complete cycle is equal to 2/π times of its maximum velocity
[D] root mean square velocity is 1/√2 times of its maximum velocity
Answer: A, B, D

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(3) The displacement time graph of a particle executing SHM is shown in the figure. Which of the following statement is/are true?

[A] the force is zero at t = 3T/4
[B] the acceleration is maximum at t = 4T/4
[C] the velocity is maximum at t = T/4
[D] the PE is equal to KE of oscillation t = T/2
Answer: A, B, C
(4) Which of the following statements is/are true for a simple harmonic oscillator?
[A] force acting is directly proportional to the displacement from the mean position and opposite to it
[B] motion is periodic
[C] acceleration of the oscillator is constant
[D] the velocity is periodic
Answer: A, B, D
(5) Displacement versus time curve for a particle executing SHM is shown in the figure. Choose the correct statements.

[A] phase of the oscillator is same at t = 0 s and t = 2 s
[B] phase of the oscillator is the same at t = 2 s and t = 6 s
[C] phase of the oscillator is the same at t = 1 s and t = 7 s
[D] phase of the oscillator is the same at t = 1 s and t = 5 s
Answer: B, D
(6) The motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is
[A] simple harmonic motion
[B] non-periodic motion
[C] periodic motion
[D] periodic but not SHM
Answer: A, B
(7) The rotation of the earth about its axis is
[A] periodic motion
[B] simple harmonic motion
[C] periodic but not simple harmonic motion
[D] non-periodic motion
Answer: A, C
(8) A particle executing SHM has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s2. The period of oscillation is
[A] πs
[B] π/2 s
[C] 2 πs
[D] π/t s
Answer: πs
(9) The equation of motion of a particle is x = a cos (αt)2. The motion is
[A] periodic but not oscillatory
[B] periodic and oscillatory
[C] oscillatory but not periodic
[D] neither periodic nor oscillatory
Answer: oscillatory but not periodic
(10) Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution, and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is

[A] x(t) = B sin (2πt/30)
[B] x(t) = B cos (πt/15)
[C] x(t) = B sin (πt/15 + π/2)
[D] x(t) = B cos (πt/15 + π/2)
Answer: x(t) = B sin (2πt/30)
(11) Four pendulums A, B, C, and D are suspended from the same elastic support as shown in the figure. A and C are of the same length, while B is smaller than A and D is larger than A. If A is given a transverse displacement,

[A] D will vibrate with maximum amplitude
[B] C will vibrate with maximum amplitude
[C] B will vibrate with maximum amplitude
[D] all the four will oscillate with equal amplitude
Answer: C will vibrate with maximum amplitude
(12) The displacement of a particle varies with time according to the relation y = a sin ωt + b cos ωt
[A] the motion is oscillatory but not SHM
[B] the motion is SHM with amplitude a + b
[C] the motion is SHM with amplitude a2 + b2
[D] the motion is SHM with amplitude √a2 + b2
Answer: the motion is SHM with amplitude √a2 + b2
(13) A particle is acted simultaneously by mutually perpendicular simple harmonic motions x = a cos ωt and y = a sin ωt. The trajectory of motion of the particle will be
[A] an ellipse
[B] a parabola
[C] a circle
[D] a straight line
Answer: a circle
(14) Motion of an oscillating liquid column in a U-tube is
[A] periodic but not simple harmonic
[B] non-periodic
[C] simple harmonic and time period is independent of the density of the liquid
[D] simple harmonic and time period is directly proportional to the density of the liquid
Answer: simple harmonic and time period is independent of the density of the liquid
(15) The relation between acceleration and displacement of four particles are given below:
[A] ax = +2x
[B] ax = +2x2
[C] ax = -2x2
[D] ax = -2x
Answer: ax = -2x
(16) The displacement of a particle is represented by the equation y = sin3 ωt. The motion is
[A] non-periodic
[B] periodic but not simple harmonic
[C] simple harmonic with period 2π/ω
[D] simple harmonic with period π/ω
Answer: simple harmonic with period 2π/ω
(17) The displacement of a particle is represented by the equation y = 3 cos(π/4 – 2ωt). The motion of the particle is
[A] simple harmonic with period 2p/w
[B] simple harmonic with period π/ω
[C] periodic but not simple harmonic
[D] non-periodic
Answer: simple harmonic with period π/ω
(18) Which of the following does not exhibit polarization
[A] Longitudinal wave in a gas
[B] Transverse wave in a gas
[C] Neither (a) nor (b)
[D] Both (a) and (b)
Answer: Longitudinal wave in a gas
(19) he length of the pendulum which is displaying SHM is increased by 21%. Calculate the percentage increase in the periodic time of the pendulum.
[A] 21%
[B] 10%
[C] 11%
[D] 42%
Answer: 10%
(20) The observer hears a sound from the source which is moving away from the observer who is stationary. Determine the frequency of the sound
[A] It is halved
[B] It remains the same
[C] It reaches infinity
[D] It gets doubled
Answer: It is halved

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