Oscillations is a core and high-weightage chapter in Class 11 Physics that introduces students to periodic and oscillatory motion. This chapter explains key concepts such as simple harmonic motion (SHM), displacement, velocity and acceleration in SHM, time period, frequency, phase, energy in SHM, spring–mass system, simple pendulum, and damped and forced oscillations. These topics are important for Class 11 exams and competitive exams like JEE and NEET.
NCERT Solutions for Class 11 Physics Chapter 13 – Oscillations are prepared strictly according to the latest CBSE syllabus and exam pattern. The solutions are written in simple, step-by-step language with clear derivations, graphs, and solved numericals, helping students build strong conceptual clarity and score well in school examinations.
NCERT Solutions for Class 11 Physics Chapter 13 – Oscillations
Q.
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 center of mass.
(d) An arrow released from a bow.
Q.
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 anticlockwise in every case: (x is in cm and t is in s).
(a) x = –2 sin (3t + p /3)
(b) x = cos (p/6 – t)
(c) x = 3 sin (2pt + p/4)
(d) x = 2 cos pt
Q.
One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the column of mercury in the U-tube executes simple harmonic motion.
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Q.
A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period?
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Q.
The acceleration due to gravity on the surface of moon is 1.7 ms–2. What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s? (g on the surface of earth is 9.8 ms–2)
Q.
The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed?
Q.
Figure 14.26 (a) shows a spring of force constant k clamped rigidly at one end and a mass m attached to its free end. A force F applied at the free end stretches the spring. Figure 14.26 (b) shows the same spring with both ends free and attached to a mass m at either end. Each end of the spring in Fig. 14.26(b) is stretched by the same force F.
(a) What is the maximum extension of the spring in the two cases?
(b)If the mass in Fig. (a) and the two masses in Fig. (b) are released, what is the period of oscillation in each case?
Q.
Figures 14.25 correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on each figure.
Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P, in each case.
Q.
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 lower most point.
(d) general vibrations of a polyatomic molecule about its equilibrium position.
Q.
In Exercise 14.9, let us take the position of mass when the spring is unstretched as x = 0, and the direction from left to right as the positive direction of x-axis. Give x as a function of time t for the oscillating mass if at the moment we start the stopwatch (t = 0), the mass is
(a) at the mean position,
(b) at the maximum stretched position, and
(c) at the maximum compressed position.
In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?
Q.
A spring having with a spring constant 1200 Nm–1 is mounted on a horizontal table as shown in Fig. 14.24. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.
Determine (i) the frequency of oscillations, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.
Q.
A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?
Q.
The motion of a particle executing simple harmonic motion is described by the displacement function,
x (t) = A cos (ωt + Φ).
If the initial (t = 0) position of the particle is 1 cm and its initial velocity is ω cms-1, what are its amplitude and initial phase angle? The angular frequency of the particle is πs–1. If instead of the cosine function, we choose the sine function to describe the SHM: x = B sin (ωt + α), what are the amplitude and initial phase of the particle with the above initial conditions.
Q.
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 = –200x2
(c) a = –10x
(d) a = 100x3
Q.
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
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Fig. 14.23 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)?
Q.
An air chamber of volume V has a neck area of cross section a into which a ball of mass m just fits and can move up and down without any friction (Fig.14.27). Show 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 [see Fig. 14.27]
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 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) Not periodic. Although the motion is to-and-fro, the time period is not definite because the swimmer may not take the same time in each trip.
(b) Periodic. A freely suspended magnet oscillates about its equilibrium (N–S) direction with a definite time period.
(c) Periodic. A rotating hydrogen molecule returns to the same position (orientation) after a fixed interval repeatedly.
(d) Not periodic. The arrow moves forward and does not repeat its motion.
Q.2) Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
(a) 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 lowest point.
(d) General vibrations of a polyatomic molecule about its equilibrium position.
Answer:
(a) Periodic but not SHM. Earth repeats its position after a fixed time, but it is not a to-and-fro motion about a mean position.
(b) (Nearly) SHM. The mercury column oscillates to-and-fro about the mean position with a definite time period.
(c) (Nearly) SHM (for small displacements). The ball executes to-and-fro motion about the lowest point and repeats after equal intervals.
(d) Periodic but not a single SHM. A polyatomic molecule has many natural frequencies; its overall motion is a superposition of several SHMs.
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 (if periodic)?
Answer:
(a) Not periodic because the motion does not repeat itself.
(b) Periodic. The motion repeats after every 2 s, so the period is 2 s.
(c) Not periodic. The particle repeats only at one position; in periodic motion, the entire motion repeats after equal intervals.
(d) Periodic. The motion repeats after 2 s, so the period is 2 s.
Q.4) A particle is in linear SHM between two points A and B, 10 cm apart. Take the direction from A to B as positive. Give the signs of velocity, acceleration and force when the particle is:
(a) at end A
(b) at 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
(f) at 4 cm away from B going towards A
Answer:
(a) At end A: Velocity = 0 (momentarily at rest). Acceleration is towards mean position (towards B), so positive. Force is also positive.
(b) At end B: Velocity = 0 (momentarily at rest). Acceleration is towards mean position (towards A), so negative. Force is also negative.
(c) At mid-point (mean position) going towards A: Velocity is towards A, so negative. At mean position, acceleration = 0 and force = 0.
(d) 2 cm away from B going towards A: Motion is towards A, so velocity is negative. Since the displacement is on the B side, restoring acceleration is towards A, so acceleration is negative. Force is also negative.
(e) 3 cm away from A going towards B: Motion is towards B, so velocity is positive. Since the displacement is on the A side, restoring acceleration is towards B, so acceleration is positive. Force is also positive.
(f) 4 cm away from B going towards A: Same as case (d). Velocity negative, acceleration negative, force negative.
Q.5) Which of the following relationships between the acceleration (a) and displacement (x) involve SHM?
(a) a = 0.7x
(b) a = −200x2
(c) a = −10x
(d) a = 100x3
Answer:
In SHM, acceleration is proportional to displacement and opposite in direction:
a = −kx
Only option (c) matches this form. Therefore, relation (c) represents SHM.
FAQs: Class 11 Physics Chapter 13 – Oscillations
Q1. Is Oscillations important for exams?
Yes, it is a high-weightage chapter in mechanics and waves.
Q2. Which topics are most important in this chapter?
Simple harmonic motion, time period, energy in SHM, and simple pendulum.
Q3. Are numericals asked from this chapter?
Yes, SHM and pendulum-based numericals are very common.
Q4. Are graphs important here?
Yes, displacement-time and velocity-time graphs are frequently asked.
Q5. How do NCERT Solutions help?
They provide NCERT-aligned, exam-ready explanations with solved numericals.