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CBSE

Class 11

Physics NCERT Book

Chapter 14:

Master Oscillations in Class 11 Physics: Complete NCERT Guide (2025-26)

Q: 4. What would happen to the time period of a simple pendulum if it were placed inside an artificial satellite orbiting the Earth? Explain why.

The time period of a simple pendulum would become infinite, which means it would not oscillate. The formula for the time period is T = 2π√(L/g). Inside an orbiting satellite, the system experiences a state of effective weightlessness, where the effective acceleration due to gravity, 'g', is zero. As g approaches zero in the formula, the time period T approaches infinity. Therefore, there is no restoring force to bring the pendulum bob back to its mean position.

Essential Study Material for CBSE Class 11 Physics Oscillations Chapter

You will study Oscillation and oscillatory motion in this Chapter. The distinction between periodic and Oscillatory Motion will be discussed. Simple Harmonic Motion and Uniform Circular Motion are also covered in this Chapter. In basic Harmonic Motion, we'll look at the notions of Velocity and Acceleration. The fundamentals of Force and Energy in Simple Harmonic Motion are also discussed in-depth in this Chapter. Finally, it discusses the notions of forced Oscillations and resonance.

NCERT Lessons for Class 11 Physics Chapter 14 are created to assist students in focusing on the most significant subjects. Every element is meticulously described to increase students' conceptual understanding. The answers also include a variety of shortcut approaches for efficiently remembering the principles. While answering textbook problems, students can refer to the solutions and comprehend the manner of answering them without trouble.

Overview of Oscillations

Periodic Motion - Periodic motions, processes, or events are those that repeat themselves at regular intervals.

Oscillatory motion - Oscillatory motion is defined as the movement of a body around a fixed point after regular intervals of time. The mean position or equilibrium position is the fixed position around which the body oscillates.

Simple harmonic motion - Simple harmonic motion is a sort of periodic oscillatory motion in which the particle I oscillates down a straight line and the particle's acceleration is always directed towards a fixed point on the line. The particle's movement from the fixed point determines the magnitude of acceleration.

Characteristics of SHM - \[\mathrm{x=A\left ( \sin \omega t + \phi \right ) }\] gives the displacement x in SHM at time t, where the three constants A, and differentiate one SHM from another. A cosine function may also be used to define an SHM:

\[\mathrm{x=A\left ( \cos \omega t + \delta \right ) }\]

At any point in time, the displacement of an oscillating particle equals the change in its position vector. "Displacement Amplitude" or "Simple Amplitude" refers to the highest magnitude of displacement in an Oscillatory Motion on each side of its mean position.

As a result, Amplitude A = x max.

\[T=2\pi \sqrt{\frac{m}{k}}\] where, k is the force constant (or spring factor) of spring.

Frequency - Frequency is defined as the number of Oscillations per second. It is measured in seconds per second or Hertz per second. Amplitude has no bearing on Frequency or Time Period.

Frequency(v)= \[\frac{1}{Time Period}\left ( \frac{1}{T} \right )\]

Phrase - The amount \[\mathrm{\left ( \omega t + \phi \right ) }\] is known as the SHM Phase at time t, and it defines the state of motion at that moment. The amount is the Phase at time f = 0 and is referred to as the SHM's Phase Constant, Starting Phase, or Epoch. In the cosine or sine function, the phase constant is the time-independent term.

If displacement of SHM is given by

\[\mathrm{x = A\sin \left ( \omega t\pm \phi \right ), then }\]

Particle Velocity \[\mathrm{v=\frac{\mathrm{d} x}{\mathrm{d} t} = \omega A\cos \left ( \omega t\pm \phi \right )}\]

\[\mathrm{v=\omega A\sqrt{1-\sin ^{2}\left ( \omega t\pm \phi \right )}=\omega A\sqrt{1-\left ( \frac{x^{2}}{A^{2}} \right )}=\omega \sqrt{A^{2}-x^{2}}}\]

Velocity Amplitude of SHM is equal to \[A\omega\]. Moreover, the particle velocity is ahead of displacement of the particle by an angle of \[\mathrm{\frac{\pi }{2}}\]

Phase Difference between displacement and velocity is \[\mathrm{\frac{\pi }{2}}\]

Acceleration of the particle executing S.H.M is given by

\[\mathrm{a= -\omega ^{2}A\sin \left ( \omega t \pm \phi \right )=-\omega ^{2}A}\]

Phase Difference between displacement and acceleration is π

The restorative force is in charge of keeping the S.H.M. in good working order.

The Restoring Force (F) exerted on the body is given by F = -kx if the displacement (x) from the equilibrium position is modest where k is a constant of force.

Energy in S.H.M. - The energy of a body that performs SHM alternates between Kinetic and Potential, while the overall energy remains constant. When x is moved away from the equilibrium position:

Time Period and Frequencyof a particle executing S.H.M may be expressed in the following way

\[\mathrm{\textrm{Total Period,T} =2\pi \sqrt{\frac{displacement}{acceleration}}}\]

\[\mathrm{\textrm{Total Period,}\upsilon =\frac{1}{2\pi }\sqrt{\frac{displacement}{acceleration}}}\]

In general, the time period and frequency can be expressed as

\[\mathrm{T =2\pi \sqrt{\frac{displacement}{acceleration}}}\]

\[\mathrm{\upsilon =\frac{1}{2\pi }\sqrt{\frac{displacement}{acceleration}}}\]

Springs in series - If two springs with spring constants k1 and k2 are connected in series, the combination's spring constant is given by

\[\mathrm{\frac{1}{k}=\frac{1}{k_{1}}+\frac{1}{k_{2}}}\]

Subtopics of Oscillations

Introduction
Periodic and oscillatory motions
Simple harmonic motion
Simple harmonic motion and uniform circular motion
Velocity and acceleration in simple harmonic motion
Force law for simple harmonic motion
Energy in simple harmonic motion
Some systems executing SHM
Damped simple harmonic motion
Forced Oscillations and resonance

FAQs on Master Oscillations in Class 11 Physics: Complete NCERT Guide (2025-26)

1. What are some expected 1-mark and 2-mark important questions from Chapter 14 Oscillations for the Class 11 exam?

For the CBSE 2025-26 exams, important short-answer questions from Oscillations often include:

Defining Simple Harmonic Motion (SHM) and stating its necessary conditions.
Explaining the phase relationship between displacement, velocity, and acceleration in SHM.
Differentiating between free, damped, and forced oscillations with one example each.
Defining a seconds pendulum and stating its effective length on Earth.

2. Why is the small-angle approximation (sinθ ≈ θ) crucial for a simple pendulum to be considered an example of Simple Harmonic Motion?

This approximation is a very important concept for exams. The restoring force for a pendulum is F = -mg sinθ. For the motion to be true SHM, the restoring force must be directly proportional to the displacement (F ∝ -θ). The approximation sinθ ≈ θ (for small angles measured in radians) linearizes the force equation to F ≈ -mgθ. Without this, the restoring force is not directly proportional to the angular displacement, making the motion oscillatory but not simple harmonic. As a result, its time period would depend on the amplitude of oscillation.

3. How can you derive the expression for the total energy of a particle in SHM and prove that it remains constant?

This is a frequently asked 3-mark or 5-mark question. The steps are as follows:
The energy of a particle in SHM is composed of Potential and Kinetic Energy.

Potential Energy (U): U = (1/2)kx² = (1/2)mω²A²cos²(ωt + φ)
Kinetic Energy (K): K = (1/2)mv² = (1/2)mω²(A² - x²)
The Total Energy (E) is the sum E = K + U.
E = (1/2)mω²(A² - x²) + (1/2)mω²x²
E = (1/2)mω²A² - (1/2)mω²x² + (1/2)mω²x²
This simplifies to E = (1/2)mω²A².

Since mass (m), angular frequency (ω), and amplitude (A) are constants for a given SHM, the total energy is conserved and does not depend on displacement (x) or time (t).

4. What would happen to the time period of a simple pendulum if it were placed inside an artificial satellite orbiting the Earth? Explain why.

The time period of a simple pendulum would become infinite, which means it would not oscillate. The formula for the time period is T = 2π√(L/g). Inside an orbiting satellite, the system experiences a state of effective weightlessness, where the effective acceleration due to gravity, 'g', is zero. As g approaches zero in the formula, the time period T approaches infinity. Therefore, there is no restoring force to bring the pendulum bob back to its mean position.

5. What is the phase difference between displacement, velocity, and acceleration in SHM? This is a very important question for Class 11 exams.

In Simple Harmonic Motion (SHM), the phase relationships are fundamental:

Velocity leads displacement by a phase angle of π/2 radians (90°). This means when displacement is at its maximum, velocity is zero.
Acceleration leads velocity by another phase angle of π/2 radians (90°).
Consequently, acceleration leads displacement by a total phase angle of π radians (180°), indicating that acceleration is always directed opposite to the displacement.

6. If a spring-mass system is oscillating vertically on Earth, what change would be observed in its time period if the entire setup is moved to the Moon?

This is a common conceptual trap question. The time period of a spring-mass system will remain unchanged. The formula for its time period is T = 2π√(m/k), where 'm' is the mass and 'k' is the spring constant. This expression does not depend on the acceleration due to gravity 'g'. Unlike a simple pendulum, the restoring force in a spring is determined by its stiffness (k) and not gravity. Therefore, moving the system to the moon, where 'g' is much lower, has no effect on its oscillation period.

7. How is the frequency of Kinetic Energy (KE) and Potential Energy (PE) related to the frequency of oscillation in SHM?

The frequency of variation for both kinetic energy and potential energy is twice the frequency of the particle's oscillation in SHM. During one complete oscillation, the particle passes through its maximum velocity (maximum KE) twice and its maximum displacement (maximum PE) twice. Therefore, if the frequency of SHM is 'f', the frequency with which the energy transforms and repeats its cycle is 2f.

8. Outline the key steps to derive the expression for the time period of a simple pendulum, a likely 5-mark question.

The derivation for the time period of a simple pendulum (T = 2π√(L/g)) involves these essential steps:

1. Identify the Restoring Force: The component of gravity that pulls the bob back to the mean position is the restoring force, F = -mg sinθ.
2. Apply the Small Angle Approximation: For small angles, we assume sinθ ≈ θ. The force equation becomes F ≈ -mgθ.
3. Relate Displacement and Angle: The linear displacement 'x' is related to the angular displacement 'θ' by x = Lθ, which gives θ = x/L.
4. Form the SHM Equation: Substitute θ to get F = -(mg/L)x. This equation is in the standard SHM form F = -Kx, where the effective force constant is K = mg/L.
5. Use the Time Period Formula: Finally, substitute this value of K into the general time period formula T = 2π√(m/K) to arrive at T = 2π√(L/g).

9. Explain why resonance is an important phenomenon with both useful and destructive real-world applications.

Resonance is the tendency of a system to oscillate with a much larger amplitude when it is driven by an external periodic force at a frequency that matches its own natural frequency. This concept is important for exams.

Useful Applications: It is used in tuning radios to a specific station's frequency. In medicine, Magnetic Resonance Imaging (MRI) uses the principle of nuclear magnetic resonance to create detailed images of the body.
Destructive Applications: Uncontrolled resonance can be dangerous. Soldiers break step when crossing a suspension bridge to avoid matching its natural frequency, which could cause it to sway violently and collapse (like the Tacoma Narrows Bridge). Similarly, earthquakes can destroy buildings if their seismic wave frequency matches the building's natural frequency.