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Oscillations Notes With JEE NEET MCQS Physics Class 11 CBSE Study Material Full Chapter Download pdf-Anand Classes

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What are Oscillations?

Oscillation is a measure of some repetitive variation, as a function of time. It can be measured with respect to a state of equilibrium. The most common and simplest example of oscillation is the motion of a simple pendulum.

Oscillatory Motion Formula

A motion is said to be oscillatory if it is repetitive in which an object repeats the same movement over and over. In the absence of friction, the body can be in oscillation forever. But in reality, the system settles in the state of equilibrium eventually. Let’s learn the calculation of the frequency of oscillatory motion.

Example: loaded spring, the motion of a pendulum

Here the frequency of the oscillatory motion is calculated by

f = 1/T

Where,

f = frequency measured in Hz

one hertz is equal to one oscillation cycle per second

T = time period of motion of waves

Oscillations Notes With JEE NEET MCQS Physics Class 11 CBSE Study Material Full Chapter Download pdf-Anand Classes

What are the three main types of Simple Harmonic Motion?

The three main types of simple harmonic motion in physics are:

Free Oscillation
Forced Oscillation
Damped Oscillations

Free Oscillation

Here, the amplitude and time period remain constant without any influence of external factors. When the system has zero damping, the amplitude remains constant provided, this theory is possible in cases where damping always occurs.

In order to overcome external forces like air resistance or friction, the reduction in amplitude(energy loss of a system) is referred to as damping. As a result, the amplitude, frequency, and energy all remain constant.

Forced Oscillation

When an external periodic force influences a body’s oscillation, then it is called forced oscillation. Here, damping occurs in the amplitude of oscillation but remains constant with the help of the external energy supplied by the system.

For example, constantly pushing a swing so that its oscillation doesn’t reduce.

Damped Oscillation

The reduction of the amplitude of an object with respect to time, such type of oscillations are known as damped oscillations. The energy of a system decreases with the decrease in amplitude. There are two types of damping:

Natural Damping
Artificial Damping

Resonance

It is the phenomenon wherein an external vibrating system causes the oscillation of another system with a higher amplitude at a particular frequency. The frequency at that particular resonance level is known as a resonant frequency. For instance, when tuning a guitar with the help of another guitar, the resonant frequency can be observed. In this case, the amplitude of the vibration of the string is the highest. The reason for large amplitude oscillations generated at that resonant frequencies are as a result of vibrational energy that is accumulated in the system. Resonance is of the following types:

Mechanical
Acoustic
Orbital
Particle
Electrical
Optical Resonance

Oscillations Notes With JEE NEET MCQS Physics Class 11 CBSE Study Material Full Chapter Download pdf-Anand Classes

Energy in Simple Harmonic Motion

Oscillations are repetitive variations that are periodic. Oscillations are measured about a point of equilibrium, also known as central value or between two or more different states. Repeating variations of any quantity or measure about its equilibrium value in time is defined as oscillation. Oscillations also occur in dynamic systems or, more accurately, in every field of science.

Example: The movement of a simple pendulum in a clock.

Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. SHM is a special case of oscillation in which motion takes place along a straight line between the two extreme points. A restoring force is seen directed towards the mean position or towards the equilibrium position in SHM. The mean position in simple harmonic motion is a stable equilibrium.

Note: All the SHM are oscillatory and periodic.

Every oscillatory motion is not a simple harmonic motion.

We can note there involves a continuous interchange of potential and kinetic energy in a simple harmonic motion. The system that performs simple harmonic motion is called the harmonic oscillator.

Case 1: The potential energy is zero, and the kinetic energy is maximum at the equilibrium point where zero displacement takes place.

Case 2: The potential energy is maximum, and the kinetic energy is zero, at a maximum displacement point from the equilibrium point.

Case 3: The motion of the oscillating body has different values of potential and kinetic energy at other points.

Oscillations Notes With JEE NEET MCQS Physics Class 11 CBSE Study Material Full Chapter Download pdf-Anand Classes

Frequently Asked Questions on CBSE Class 11 Physics Notes Chapter Oscillations

What is the meaning of oscillatory motion?

A motion repeating itself is referred to as periodic or oscillatory motion.

What is resonance?

Resonance describes the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force is equal or close to the natural frequency of the system on which it acts.

What is acoustic sound?

Acoustics is the science related to the production, control, transmission, reception and effects of sound.

Short Notes of Chapter Oscillations Class 11 Physics download pdf free

1. Oscillatory Motion:

Oscillatory motion is repetitive and periodic.
Examples include the motion of a pendulum, a vibrating guitar string, or a mass-spring system.

2. Simple Harmonic Motion (SHM):

SHM is a special type of oscillatory motion.
It is characterized by a restoring force proportional to the displacement and directed opposite to it.
Examples include the motion of a mass on a spring and a simple pendulum.

3. Characteristics of SHM:

Amplitude (A): Maximum displacement from the equilibrium position.
Frequency (f): Number of oscillations per unit time (measured in Hertz, Hz).
Period (T): Time taken to complete one oscillation (T = 1/f).

4. Equations of SHM:

Displacement ( $x$ ) as a function of time ( $t$ ): $x (t) = A \cdot cos (2 π f t + ϕ)$
Here, $ϕ$ is the phase constant.

5. Energy in SHM:

Total mechanical energy ( $E$ ) remains constant in SHM.
$E =1/ 2 m ω^{2} A^{2}$ , where $k$ is the spring constant and $ω$ is the angular frequency.

6. Pendulum Motion:

The period of a simple pendulum ( $T$ ) is given by $T = 2 π(L/g) 1/2$ , where $L$ is the length and $g$ is the acceleration due to gravity.

7. Damped Oscillations:

Damping involves a resistive force that reduces the amplitude of oscillation.
Overdamping, underdamping, and critical damping are different damping scenarios.

8. Forced Oscillations:

Oscillations under the influence of an external force.
Resonance occurs when the frequency of the external force matches the natural frequency of the system.

9. Wave Motion:

Oscillations can result in wave motion.
Transverse waves have oscillations perpendicular to the direction of wave propagation, while longitudinal waves have oscillations parallel to the direction of wave propagation.

10. Applications:

Oscillatory motion is prevalent in various fields, from mechanical systems to electromagnetic waves.

11. Resonance:

Resonance occurs when a system is subjected to a periodic force at its natural frequency, leading to a large amplitude response.
Commonly observed in musical instruments and structural engineering.

12. Phase and Phase Difference:

Phase represents the position of an oscillating object at a specific point in time.
Phase difference ( $δ$ ) is the measure of the relative positions of two oscillating objects at a given instant.

13. Simple Pendulum:

The motion of a simple pendulum can be approximated as SHM for small angles.
The restoring force is provided by the component of gravity perpendicular to the pendulum’s motion.

14. Angular Frequency ( $ω$ ):

Angular frequency ( $ω$ ) is related to the frequency ( $f$ ) by $ω = 2 π f$ .
It determines the rate of change of phase with respect to time.

15. Beats:

Beats result from the superposition of two slightly different frequencies.
The beat frequency is the difference between the frequencies of the two waves.

16. Lissajous Figures:

Lissajous figures are graphical representations of complex harmonic motion.
They are formed when two perpendicular simple harmonic motions are graphed against each other.

17. Wave Equation:

Describes the behavior of a wave.
For a wave traveling in the x-direction: $y (x, t) = A sin (k x - ω t + ϕ)$ , where $k$ is the wave number and $ϕ$ is the phase constant.

18. Doppler Effect:

Change in frequency or wavelength of a wave in relation to an observer moving relative to the source of the wave.
Applicable to both sound and light waves.

19. Standing Waves:

Formed by the interference of two identical waves traveling in opposite directions.
Nodes and antinodes are characteristic points on a standing wave.

20. Applications in Medicine and Engineering:

Oscillatory principles are applied in medical instruments, such as ultrasound, and engineering fields like telecommunications and signal processing.

21. Quantum Oscillations:

Quantum mechanics introduces oscillatory behavior at the atomic and subatomic levels.
Examples include atomic orbitals and electronic oscillations.

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