Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Waves and oscillations → Simple Harmonic Motion ↓


Resonance and applications


Simple harmonic motion (SHM) is a fascinating concept in physics that describes certain repetitive or oscillatory motions. It is fundamental to understanding a variety of physical phenomena, from the swinging of a pendulum to complex wave patterns. Here, we focus on a particular aspect of this motion: resonance.

Understanding simple harmonic motion (SHM)

In simple terms, SHM is a type of motion in which an object moves back and forth. This motion is periodic, which means it occurs at regular intervals. A great example of this is a swinging pendulum or a mass attached to a spring. Let's get a little technical now.

An object undergoing simple harmonic motion experiences a force that is directly proportional to its displacement from its equilibrium position and is directed towards that position. It can be described by the formula:

F = -kx

Here, F is the force, k is the spring constant, and x is the displacement. The negative sign indicates that the force is restorative—it acts to bring the object back to its starting point.

The object moves along a regular, repeating path. The time it takes to complete one full cycle of motion is called the period, denoted by T. Another related concept is the frequency, f, which represents how many cycles occur in one second.

Illustration of SHM

A B C

In the above illustration, points A, B, and C represent different positions of an oscillating object. When the object is located at B, it is in equilibrium. The maximum displacement occurs at points A and C.

Explanation of resonance

Resonance is a special condition in oscillatory systems such as SHM, which refers to vibrations of a large amplitude when a system is driven at its natural frequency. The natural frequency is the rate at which the system vibrates when a constant or repeated external force is not applied to it.

In real life, resonance can be observed in several scenarios:

  • When pushing someone on a swing, if you apply force in sync with the natural motion of the swing, it causes the swing to rise higher.
  • Musical instruments such as guitars have strings that vibrate at natural frequencies. The sound box amplifies these vibrations in harmony, due to resonance.

Resonance visualization

General Dimensions Echo

The figure above shows two systems. On the left, the yellow circle represents a system under normal conditions. On the right, the red circle represents a system undergoing resonance, characterized by increased amplitude.

The science behind resonance

When we talk about moving a system or producing forced motion, we are talking about an external force applied to it. If this force is aligned with the natural frequency of the system, the energy transfer efficiency is at its peak. It is like being perfectly synchronized with a person swinging your ass to lift your ass up in the air.

Resonance is exceptionally efficient in the transfer of energy. The applied forces do more work, resulting in a larger magnitude or amplitude of the resulting motion. Mathematically:

        A(t) = A_0 cos(ωt + φ)

In this equation, A(t) is the displacement at time t, A_0 is the maximum amplitude, ω is the angular frequency, and φ is the phase angle.

Applications of resonance

There are many practical applications of resonance:

  • Musical instruments: Resonance adds richness to music. Instruments such as the piano and violin use resonance to amplify the sound.
  • Tuning Forks: These are precision instruments based on resonance that help musicians tune instruments by providing a certain frequency.
  • Radio Tuner: Radios use resonance circuits to select the desired market frequencies, allowing you to listen to your favorite channels.

Effects of resonance in construction

Resonance is a double-edged sword. Although it is beneficial, it can lead to disastrous consequences such as collapse of structures. Resonance is carefully considered during the design of buildings and bridges to ensure that they can withstand the natural frequencies during earthquakes or high winds.

Examples of resonance in daily life

Example 1: Pushing a Swing When you time your pushes on the swing perfectly with its motion, the swing reaches high amplitudes, demonstrating resonance.

Example 2: Microwave ovens work on the principle of microwave resonance where they excite water molecules in the food, producing heat to cook the food evenly.

Example 3: Glass and sound Singing at a certain frequency can break glass. This is because the singing tone causes the glass to resonate excessively, causing the glass to shatter when the amplitude exceeds structural limits.

Conclusion

Resonance is a fascinating phenomenon intertwined with the fabric of harmonic motion, which has many applications that are not only theoretical but also practical. From the tuning of musical instruments to the communication devices we use every day, resonance bridges the gap in the physical world and leads to both beneficial and dangerous results depending on its use.


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Resonance and applications

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