Periodic motions are those motions where movements are repeated after a specific time interval. This specific interval of time is termed as the time period of the concerned periodic motions. A very common example of periodic motion is the movements of the hands of a clock. Whereas in oscillatory motions, to and fro movements occur about a fixed position, that is, the point of equilibrium. Thus, oscillation is also a kind of periodic motion, but all periodic motions are not oscillatory motions.

In technical language, Simple Harmonic Motion or SHM (in short) is termed for a motion where the restoring or reinstating force remains proportional directly to the displacement of an object from its mean position. The direction of the above-said force always remains towards the concerned object's mean position. Like in any other motion, acceleration is also acted upon the particles undergoing simple harmonic motion and it is represented by the following formula: a(t) = -ω² x(t), where ω represents the angular velocity of the particles. Simple harmonic motion is a special type of oscillatory motion. There are two categories of simple harmonic motion, linear and angular.

Uniform circular motion is nothing but an interpretation of simple harmonic motion. Imagine a stone being vertically hung from a point with a string, and you move it in such a way that it moves along a circular path. The point to which this string is tied acts as the centre for this circular path of rotation. Now a person who is watching this movement from the top will see a uniform circular motion occurring due to the rotating stone. For another person, who is standing at the plane on which the stone is rotating, the stone will appear to move in a characteristic simple harmonic motion. Therefore, it can also be said that a simple harmonic motion is nothing but a uniform circular motion being projected on the diameter of a circle of concern.

When there is acceleration in the motion of a particle, the velocity is bound to keep on changing. In the case of simple harmonic motion, the same motion is performed by the particle under observation repeatedly over a specific time period. From previous knowledge, we know that acceleration is velocity per unit of time. The acceleration of simple harmonic motion is given by the formula: d²x/dt² = – ω²x, where d²x/dt² represents the acceleration of the particle under consideration, x stands for the displacement of the particle and ω represents angular frequency.

Before we get into the force law for simple harmonic motion, let us know what a restoring force is. A force that is directly proportional to the displacement of the particle but always acts in a direction opposite to it. Restoring force is attains its maximum value when at the extremities, and upon reaching the mean position, it becomes minimum. This will come in handy as we move forward towards the equations representing the force law for simple harmonic motion. 

Considering the fact that restoring force is directly proportional to and acts in the opposite direction of displacement, the following two equations are represented:

F = – kx ……. (1). Here, k denotes the force constant, and x is the displacement. 

Since  F = ma (where m means mass and a means acceleration)

Therefore, replacing the values in the above equation 1, the following equation can be yielded:

a = – kx/m = – ω²x .……(2). As already mentioned above, ω represents angular frequency.

These two equations represent the equations of force laws for simple harmonic motion

All objects possess energy, whether at rest or be moving. While at rest, the energy inside a body is called potential energy, whereas, the energy of a moving body is called kinetic energy. During an oscillatory motion, the fundamental change happens in the state of energy. Here the potential energy gets changed into kinetic energy. One cycle of this energy change is responsible for a single oscillatory motion or oscillation cycle. Therefore, the total energy in simple harmonic motion is the sum total of potential energy and kinetic energy. It is represented by the following formula: E = 1/2 m ω²a².

Two systems that execute simple harmonic motion and are very basic and common:
I. Spring-block system: where a spring is attached to a fixed position on a wall and a block is used to exert and release the force on or from it.
II. Simple pendulum: where a heavy sphere is attached vertically to a string to a fixed point, which moves side-ways.
Students can learn details of these mentioned systems in the Class 11 Physics Oscillations NCERT Solutions book.

When the motion of an oscillator is restricted due to external force, its motion is said to be slowed down or damped. Such gradually decreasing periodic motions are called damped simple harmonic motions. A simple pendulum represents itself as a good example of damped simple harmonic motions. The energy in damped simple harmonic motions dissolves constantly.

Upon the displacement of a system from its equilibrium position on releasing or applying force, oscillations take place at a natural frequency, and such oscillations are free oscillations. Due to damping forces, the oscillations become slow gradually. The oscillations can be maintained by the application of external forces, and then such oscillations become forced or driven oscillations. Resonance is termed a phenomenon where the frequency of oscillation is increased due to external force, and it becomes closer to the naturally occurring frequency of the oscillator.

Q1. Why is Oscillations an important chapter?

Ans. The Class 11 Physics Oscillations chapter, along with the chapter Waves, carry 12 marks in total. This chapter serves as the basis for many more topics in higher classes.

Q2. What are the main features of NCERT Solutions for Class 11 Physics Chapter 14 Oscillations?

Ans. The  NCERT Solutions for Class 11 Physics Chapter 14 Oscillations offers students appropriate and accurate solutions to the questions from the chapter on oscillation. The solutions in the book are at par with the CBSE curriculum. This helps them perform well in board exams as well as other competitive exams.

Q3. Explain simple harmonic motion with examples. 

Ans. Simple harmonic motions are to and for sideways movements, where the maximum displacement on one side equals the maximum displacement of the opposite side as well. Example: a simple pendulum.

Q4. Define oscillations.

Ans. Oscillation is the repetitive movement of particles about their mean value. Vibration can be used alternatively for oscillation.