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Examples Of Simple Harmonic Motion

2. Displacement, Velocity, and Acceleration in SHM:

Equations:

  • $$Displacement, x=A\sin\omega t$$
  • $$Velocity, v=A\omega \cos \omega t$$
  • $$Acceleration, a=-A\omega^2 \sin\omega t$$ where,
  • (A) is the amplitude of oscillation.
  • (\omega) is the angular frequency of oscillation.

Graphical Representation:

(Displacement) vs. (Time) graph: [Image of a sine curve]

(Velocity versus Time) graph: [Image of a cosine curve]

(Acceleration) vs. (Time) graph: [Image of a sine curve, shifted down by (\pi/2)]

Phase and Phase Difference:

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Forces On Bodies Systems Involving Strings Or Springs

Newton’s Three Laws of Motion

  • First Law: Objects in motion stay in motion, objects at rest stay at rest, unless an external force acts on them.
  • Second Law: Force equals mass times acceleration (F = ma), or force is necessary to accelerate an object of mass m by changing its velocity with acceleration a.
  • Third Law: For each force or interaction that occurs, there is an equal and opposite force or interaction.

Tension

  • The force exerted by a string in a system is called tension force.
  • Tension force always acts away from the point where the string is held, and is equal throughout a taut (rigid) string.

Hooke’s Law

  • Hooke’s Law explains the relationship between the deformation of an elastic object (like a stretched spring) and the restoring force it exerts.
  • The force required to stretch or compress the object is directly proportional to the displacement (change in length) from its original length.
  • Mathematically, F = -kx, where k is known as the spring constant.

Simple Harmonic Motion (SHM)

  • SHM is a type of periodic motion where an object repeatedly moves back and forth through a fixed point (equilibrium position) with constant speed.
  • Key features include period (T) - time for one complete cycle; frequency (f) - number of cycles per second; amplitude (A) - maximum displacement from the equilibrium position.
  • SHM is observed in various situations like spring-mass systems, oscillating pendulums, or AC current variations.

Resonance

  • Resonance occurs when an external periodic force has a frequency that matches the natural frequency of an oscillating system.
  • It results in a significant increase in the amplitude of oscillations.
  • Applications include tuning musical instruments and designing shock absorbers to minimize vibrations.

Equilibrium of Forces

  • Equilibrium is the state of a body or system where the net force acting on it is zero.
  • To be in equilibrium, the vector sum of all forces acting on the object or system must be zero.
  • Important for understanding stability and balance in various physical situations and problem-solving.

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Forces On Bodies Contact And Non Contact Forces

Force Key Points
Normal force The force exerted by a surface perpendicular to the surface. It prevents objects from sinking into the surface.
Remember: “Normal” means “perpendicular”.
Friction The force that opposes the motion of two surfaces in contact. It is caused by the interlocking of microscopic irregularities on the surfaces.
Remember: Friction is like a “tug-of-war” between surfaces.
Tension The force exerted by a rope, cable, or other flexible object that is under tension.
Remember: Tension is like a “stretching” force.
Spring force The force exerted by a spring when it is stretched or compressed.
Remember: Springs are like “bouncy” objects that store energy.

Non-contact Forces:


Force Key Points
Gravitational force The force of attraction between two objects with mass. The greater the mass of the objects, the greater the gravitational force.
Remember: Gravity is the force that keeps us on the ground.
Electrostatic force The force of attraction or repulsion between charged particles.
Remember: Electrostatic force is like a “magnet” force, but it works with electric charges.
Magnetic force The force exerted by a magnet on a magnetic material.
Remember: Magnetic force is like a “super-strong” electrostatic force that only works with magnets.

Newton’s Laws:


Law Key Points
Newton’s first law of motion (law of inertia) An object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity in a straight line unless acted upon by an external force.
Remember: Inertia is like “laziness” - objects don’t want to change their motion.
Newton’s second law of motion (law of acceleration) The acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the mass of the object.
Remember: The more force you apply to an object, the faster it will accelerate. The more massive an object, the harder it is to accelerate.
Use the formula: (F = ma), where (F) is the net force, (m) is the object’s mass and (a) is its acceleration.
Newton’s Third law of motion (law of action and reaction) For every action, there is an equal and opposite reaction.
Remember: Actions always have “reaction partners”.

Applications of Newton’s Laws:


Application Key Points
Equilibrium of forces When the net force acting on an object is zero, the object is in equilibrium.
Remember: Equilibrium is like “balancing” forces.
Dynamics of a particle The study of the motion of a particle under the influence of forces.
Remember: Particle dynamics is like “tracing” the path of a moving particle.
Motion under gravity The study of the motion of objects under the influence of gravity.
Remember: Gravity always “pulls” objects down.
Projectile motion The study of the motion of objects launched into the air at an angle.
Remember: Projectile motion is like throwing a “ball”.
Circular motion The study of the motion of objects moving in circles.
Remember: Circular motion is like “going round and round”.
Work and energy The study of the relationship between work and energy.
Remember: Work is the “transfer of energy” between objects.
Impulse and momentum The study of the relationship between impulse and momentum.
Remember: Impulse is the “change in momentum” due to a force applied over a short time.
**Collisions The study of the interaction between objects that collide.
Remember: Collisions can be “fun” but also cause damage.

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Galilean Laws Kepler Laws Centripetal Forces Gravitation

1. Galilean Laws (Laws of Motion):

NCERT References:

  • 11th Physics: Chapter 5 - Laws of Motion
  • 12th Physics: Chapter 5 - Laws of Motion and Chapter 6 - Work, Energy, and Power
  • Key Points:
  • Explain the concepts of inertia, acceleration due to gravity, and conservation of momentum through real-life examples.
  • Derive equations related to motion under gravity and uniformly accelerated motion, including v = u + at, s = ut + ½ at², and v² – u² = 2as.
  • Understand and solve problems involving inclined planes, pulleys, and coefficients of friction.

2. Kepler’s Laws of Planetary Motion:

NCERT References:

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Human Physiology Neural Control And Coordination

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  4. Application: Connect to diseases and disorders of nervous system

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🎯 NEET Focus Areas

  • High Weightage: CNS and PNS organization (8-10 questions)
  • Important: Neuron structure and impulse transmission (6-8 questions)
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🧪 Clinical Connections

  • Alzheimer’s Disease: Neurodegeneration affecting memory
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📋 Quick Reference

  • ** resting potential**: -70mV
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