# Oscillations Chapter 14 Class 11 Physics NCERT Textbook PDF

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### Chapter 14: Oscillations

In our daily life, we come across various kinds of motions. You have already learned about some of them, e.g., rectilinear motion and motion of a projectile.

Both these motions are non-repetitive. We have also learned about the uniform circular motion and orbital motion of planets in the solar system.

In these cases, the motion is repeated after a certain interval of time, that is, it is periodic.

In your childhood, you must have enjoyed rocking in a cradle or swinging on a swing. Both these motions are repetitive in nature but different from the periodic motion of a planet.

Here, the object moves to and fro about a mean position. The pendulum of a wall clock executes
a similar motion.

Examples of such periodic to and fro motion abound: a boat tossing up and down in a river, the piston in a steam engine going back and forth, etc. Such a motion is termed oscillatory motion. In this chapter, we study this motion.

The study of oscillatory motion is basic to physics; its concepts are required for the understanding of many physical phenomena.

In musical instruments, like the sitar, the guitar, or the violin, we come across vibrating strings that produce pleasing sounds.

The membranes in drums and diaphragms in telephone and speaker systems vibrate to and fro about their mean positions.

The vibrations of air molecules make the propagation of sound possible. In a solid, the atoms vibrate about their equilibrium positions, the average energy of vibrations being proportional to temperature.

AC power supply gives voltage that oscillates alternately going positive and negative about the mean value (zero).

The description of a periodic motion, in general, and oscillatory motion, in particular, requires some fundamental concepts, like period, frequency, displacement, amplitude, and phase. These concepts are developed in the next section.

shows some periodic motions. Suppose an insect climbs up a ramp and falls down, it comes back to the initial point and repeats the process identically.

If you draw a graph of its height above the ground versus time, it would look something like Fig. 14.1 (a).

If a child climbs up a step, comes down, and repeats the process identically, its height above the ground would look like that in Fig. 14.1 (b).

When you play the game of bouncing a ball off the ground, between your palm and the ground, its height versus time graph would look like the one in Fig. 14.1 (c).

Note that both the curved parts in Fig. 14.1 (c) are sections of a parabola given by Newton’s equation of motion (see section 3.6)

### NCERT Solutions Class 11 Physics Chapter 14 Oscillations

1. Which of the following examples represents 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 center of mass.

(d) An arrow released from a bow.

Solution:

(a) The swimmers’ motion is not periodic. The motion of the swimmer between the banks of a river is to and fro. However, it does not have a definite period. This is because the time is taken by the swimmer during his back and forth journey may not be the same.

(b) The motion of a freely-suspended magnet, if displaced from its N-S direction and released, is periodic. Because the magnet oscillates about its position for a definite period of time.

(c) A hydrogen molecule rotating about its center of mass is periodic. This is because when a hydrogen molecule rotates about its center of mass, it comes to the same position again and again after an equal interval of time.

(d) An arrow released from a bow moves only in the forward direction. It does not come backward. Therefore, this motion is not periodic.

2. Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
(a) the rotation of the earth about its axis.
(b) the motion of an oscillating mercury column in a U-tube.
(c) the 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.

Solution:

(a) Rotation of the earth is not to and fro motion about a fixed point. Therefore, it is periodic but not S.H.M.
(b) Simple harmonic motion
(c) Simple harmonic motion
(d) General vibrations of a polyatomic molecule about its equilibrium position are periodic but not SHM. A polyatomic molecule has a number of natural frequencies. Therefore its vibration is a superposition of simple harmonic motions of a number of different frequencies.