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Class 11 Physics Chapter 14 - Oscillations

Last updated date: 13th Jul 2024
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Chapter 14 in Physics for Class 11

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.

Competitive Exams after 12th Science

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 Class 11 Physics Chapter 14 - Oscillations

1. When the amplitude of a basic pendulum is increased, how does this affect the time period?

No, when the amplitude of the pendulum is raised or lowered, there is no influence on the time period.

2. What is the relationship between the length of a second pendulum and the acceleration due to the gravity of any planet?

The length of the second pendulum is related to gravity's acceleration.

3. In S.H.M., what is the frequency of a particle's total energy?

S.H.M has a frequency of zero since the overall energy of the particle remains constant.

4. In S.H.M., how is the frequency of Oscillation connected to the frequency of change in the body's KE and PE?

P.E. or K.E. completes two vibrations in the time it takes S.H.M to complete one, or P.E. or K.E. has a frequency that is twice that of S.H.M.

5. Define a spring's force constant.

A spring's spring constant is equal to the change in the force it exerts divided by the change in deflection.

6. What's the difference between resonance and forced Oscillations?

In the case of forced Oscillation, the frequency of the external periodic force is different from the natural frequency of the oscillator, but in resonance, the two frequencies are identical.

7. In SHM, how do displacement, velocity, and acceleration relate to one another in terms of phase?

By a phase II in SHM, the velocity precedes the displacement. Acceleration is 2 radians ahead of velocity, while velocity is 2 radians ahead of acceleration.

8. Why is the pitch of an organ pipe higher on a hot summer day?

On a hot day, the velocity of sound will be higher because the frequency of sound increases (frequency proportional to velocity) and so its pitch increases.

9. How would the frequency change if any liquid with a density greater than that of water is employed in a resonance tube?

Vibration frequency is determined by the length of the air column rather than the reflecting material, hence frequency does not change.

10. What causes the basic pendulum to swing?

The Weight Component is the answer (mg sin)