**NCERT Solutions Class 11 Physics Chapter 14 Oscillations** – Here are all the NCERT solutions for Class 11 Physics Chapter 14. This solution contains questions, answers, images, explanations of the complete chapter 14 titled O fOscillations taught in Class 11. If you are a student of Class 11 who is using NCERT Textbook to study Physics, then you must come across chapter 14 Oscillations After you have studied the lesson, you must be looking for answers of its questions. Here you can get complete NCERT Solutions for Class 11 Physics Chapter 14 Oscillations in one place.

## NCERT Solutions Class 11 Physics Chapter 14 Oscillations

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For a better understanding of this chapter, you should also see summary of Chapter 14 Oscillations , Physics, Class 11.

Class | 11 |

Subject | Physics |

Book | Physics Part I |

Chapter Number | 14 |

Chapter Name |
Oscillations |

### NCERT Solutions Class 11 Physics chapter 14 Oscillations

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### Question & Answer

Q.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 ts N-S direction and released. (c) A hydrogen molecule rotating about its center of mass. (d) An arrow released from a bow.

Ans :(b) and (c) (a) The swimmer's motion is not periodic. The motion of the swimmer between the banks of a river is back and forth. However, it does not have a definite period. his is because the time 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. This is because the magnet oscillates about its position with a definite period of time. (c) When a hydrogen molecule rotates about its centre of mass, it comes to the same position again and again after an equal interval of time. Such motion is periodic. (d) An arrow released from a bow moves only in the forward direction. It does not come backward. Hence, this motion is not a periodic.

Q.2:Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? (a) the rotation 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.

Ans :(b) and (c) are SHMs (a) and (d) are periodic, but not SHMs (a) During its rotation about its axis, earth comes to the same position again and again in equal intervals of time. Hence, it is a periodic motion. However, this motion is not simple harmonic. This is because earth does not have a to and fro motion about its axis. (b) An oscillating mercury column in a CJ-tube is simple harmonic. This is because the mercury moves to and fro on the same path, about the fixed position, with a certain period of time. (c) The ball moves to and fro about the lowermost point of the bowl when released. Also, the ball comes back to ts initial position in the same period of time, again and again. Hence, its motion is periodic as well as simple harmonic. (d) A polyatomic molecule has many natural frequencies of oscillation. Its vibration is the superposition of individual simple harmonic motions of a number of different molecules. Hence, it is not simple harmonic, but periodic.

Q.3:depicts four x t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?

Ans :(b) and (d) are periodic (a) It is not a periodic motion. his represents a unidirectional, linear uniform motion. There is no repetition of motion in this case (b) In this case, the motion of the particle repeats itself after 2 s. Hence, It is a periodic motion, having a period of 2 s. (c) It is not a periodic motion. This is because the particle repeats the motion in one position only. For a periodic motion, the entire motion of the particle must be repeated in equal intervals of time. (d) In this case, the motion of the particle repeats itself after 2 s. Hence, it is a periodic motion, having a period of 2 s .

Q.4:Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic \(\begin{array}{l}{\text { motion }(\omega \text { is any positive constant }) :} \\ {\text { (a) } \sin \omega t-\cos \omega t} \\ {\text { (b) } \sin ^{3} \omega t} \\ {\text { (c) } 3 \cos (\pi / 4-2 \omega t)} \\ {\text { (d) } \cos \omega t+\cos 3 \omega t+\cos 5 \omega t} \\ {\text { (e) } \exp \left(-\omega^{2} t^{2}\right)}\end{array}\)

Ans :\(\begin{array}{l}{\text { (a) SHM }} \\ {\text { The given function is: }} \\ {\sin \omega t-\cos \omega t} \\ {=\sqrt{2}\left[\frac{1}{\sqrt{2}} \sin \omega t-\frac{1}{\sqrt{2}} \cos \omega t\right]} \\ {=\sqrt{2} \sin \left(\omega t-\frac{\pi}{4}\right)} \\ {=\sqrt{2} \sin \left(\omega t-\frac{\pi}{4}\right)}\end{array}\) This function represents SHM as it can be written in the form: \(a \sin (\omega t+\phi)\) Its period is : \(\frac{2 \pi}{\omega}\) \(\begin{array}{l}{\text { (b) Periodic, but not SHM }} \\ {\text { The given function is: }} \\ {\sin ^{3} \omega t} \\ {=\frac{1}{2}[3 \sin \omega t-\sin 3 \omega t]}\end{array}\) The terms \(\sin \omega t \text { and } \sin \omega t\) individually represent simple harmonic motion (SHM). However, the superposition of two SHM IS periodic and not simple harmonic. \(\begin{array}{l}{\text { (c) SHM }} \\ {\text { The given function is: }} \\ {3 \cos \left[\frac{\pi}{4}-2 \omega t\right]} \\ {=3 \cos \left[2 \omega t-\frac{\pi}{4}\right]} \\ {\text { This function represents simple harmonic motion because it can be written in the form: }} \\ {a \cos (\omega t+\phi)}\end{array}\) Its period is \(\frac{2 \pi}{2 \omega}=\frac{\pi}{\omega}\) \(\begin{array}{l}{\text { (d) Periodic, but not SHM }} \\ {\text { The given function is } \cos \omega t+\cos 3 \omega t+\cos 5 \omega t \text { . Each individual cosine function }} \\ {\text { represents SHM. However, the superposition of three simple harmonic motions is }} \\ {\text { periodic, but not simple harmonic. }}\end{array}\) \(\begin{array}{l}{\text { (e) Non-periodic motion }} \\ {\text { The given function } \exp \left(-\omega^{2} t^{2}\right)_{\text { is an exponential function. Exponential functions do not }}} \\ {\text { repeat themselves. Therefore, it is a non-periodic motion. }} \\ {\text { (f) The given function 1 }+\omega t+\omega^{2} t^{2} \text { is non-periodic. }}\end{array}\)

Q.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 direct on 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 A3 going towards A, (d) at 2 cm away from 3 going towards A, (e) at 3 cm away from A going towards B, and (f) at 4 cm away from B going towards A.

Ans :(a) Zero, Positive, Positive (b) Zero, Negative, Negative (c) Negative, Zero, Zero (d) Negative, Negative, Negative (e) Zero, Positive, Positive (f) Negative, Negative, Negative The given situation is shown in the following figure. Points A and B are the two end points, with AB = 10 cm. O is the midpoint of the path. A particle is in linear simple harmonic motion between the endpoints (a) At the extreme point A, the particle is at rest momentarily. Hence, its velocity is zero at this point. Its acceleration is positive as it is directed along AO. Force is also positive in this case as the particle is directed rightward. (b) At the extreme point B, the particle is at rest momentarily. Hence, its velocity is zero at this point. Its acceleration is negative as it is directed along 3. Force is also negative in this case as the particle is directed leftward. (c) The particle is executing a simple harmonic motion. O is the mean position of the particle. Its velocity at the mean position O is the maximum. The value for velocity is negative as the particle is directed leftward. The acceleration and force of a particle executing SHM is zero at the mean position. (d) The particle is moving toward point O from the end B. This direction of motion is opposite to the conventional positive direction, which is from A to B, Hence, the particle's velocity and acceleration, and the force on it are all negative. (e) The particle is moving toward point O from the end A. This direction of motion is from A to B, which is the conventional positive direction. Hence, the values for velocity, acceleration, and force are all positive. (f) This case is similar to the one given in (d).

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