## NCERT Solutions for Class 11 Physics Chapter 14 Oscillations

**QUESTIONS FROM TEXTBOOK** ( Oscillations Notes )

**Question 14. 1. Which of the following examples represent periodic motion?****(a) A swimmer completing one (return) trip from one bank of a river to the other and back.****(b) A freely suspended bar magnet displaced from its N-S direction and released.****(c) A hydrogen molecule rotating about its centre of mass.****(d) An arrow released from a bow.****Answer: ** (a) It is not a periodic motion. Though the motion of a swimmer is to and fro but will not have a definite period.

(b) Since a freely suspended magnet if once displaced from N-S direction and released, it oscillates about this position, it is a periodic motion.

(c) The rotating motion of a hydrogen molecule about its centre of mass is periodic.

(d) Motion of an arrow released from a bow is non-periodic.

**Question 14. 2. Which of the following examples represent (nearly) simple harmonic motion and which represent****periodic but not simple harmonic motion?****(a) the rotations of earth about its axis.****(b) motion of an oscillating mercury column in a U-tube.****(c) motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lowermost point.****(d) general vibrations of a polyatomic molecule about its equilibrium position.****Answer:** (a) Since the rotation of earth is not to and fro motion about a fixed point, thus it is periodic but not S.H.M.

(b) It is S.H.M.

(c) It is S.H.M.

(d) General vibrations of a polyatomic molecule about its equilibrium position is periodic but non SHM. In fact, it is a result of superposition of SHMs executed by individual vibrations of atoms of the molecule.

**Question 14. 5. A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is****(a) at the end A,****(b) at the end B,****(c) at the mid-point of AB going towards A,****(d) at 2 cm away from B going towards A,****(e) at 3 cm away from A going towards B, and (f) at 4 cm away from B going towards A.****Answer: ** In the fig. (given below), the points A and B, 10 cm apart, are the extreme positions of the particle in SHM, and the point O is the mean position. The direction from A to B is positive, as indicated.

**Question 14. 6. Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?****(a) a = 0.7x (b) a = – 200 x ^{2}**

**(c) a = – 10x (d) a = 100 x**

^{3}**Answer:**Only (c) i.e., a = – 10x represents SHM. This is because acceleration is proportional and opposite to displacement (x).

**Question 14. 12. Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial (t = 0) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anti-clockwise in every case:****(x is in cm and t is in s)****(a) x = – 2 sin (3t + π /3)****(b) x = cos (π /6 – t)****(c) x = 3 sin (2πt + π /4)****(d) x = 2 cos π t.**

**Question 14. 20. An air chamber of volume V has a neck area of cross-section into which a ball of mass m just fits and can move up and down without any friction (Fig.). Shaw that when the ball is pressed down a little and released, it executes SHM. Obtain an expression for the time period of oscillations assuming pressure-volume variations of air to be isothermal.**

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