SHM and Waves: Quick Revision of Formulae for IIT JEE, UPSEE & WBJEE
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Find unitwise concepts and formulae from the chapter Simple Harmonic Motion and Waves. These concepts and formulae are very important in quick revision of complete unit. Once you have gone through chapters thoroughly and understood it well there is no need to study it again and again. You can only revise important formulas and terms which will save your precious time.
These formulae will be helpful in various engineering entrance examinations. In UPSEE and WBJEE where most of questions are asked directly on formulae, this quick revision note is very important.
SHM and Waves
- Simple harmonic motion is a special type of periodic motion, in which a particle moves to and fro repeatedly about a mean position under a restoring force
- Restoring force is directly proportional to displacement of the particle from mean position
Mathematically, F = – kx
- Velocity in simple harmonic motion is defined as the time rate of change of its displacement at that instant. Mathematically,
- Acceleration in simple harmonic motion is defined as the rate of change of its velocity at that instant. Mathematically,
- Potential energy in simple harmonic motion is due to the displacement of the particle from its mean position. Mathematically,
- Kinetic energy in simple harmonic motion is due to the velocity of the particle. Mathematically,
- Total energy = Total mechanical energy = Kinetic energy + Potential energy
- Time period of simple harmonic motion is denoted by T.
where, T = Time Period, y = displacement, A = acceleration
where, T = Time Period of simple pendulum, l = length of the string, g = acceleration due to gravity
- If n springs of different force constant are connected in series having force constant k1, k2, k3... respectively then
- If n springs of different force constant are connected in parallel having force constant k1, k2, k3... respectively then
Keff = k1 + k2 + k3...
Work Function: A certain minimum amount of energy is required to be given to an electron to pull it out from the surface of the metal. This minimum energy required by an electron to escape from the metal surface is called the work function of the metal.
There are three types of electronic emissions:
(a) Thermionic emission
(b) Field emission
(c) Photo-electric emission
- All the photosensitive substances such as lithium, sodium, potassium, caesium and rubidium emit electrons when they are illuminated by light. After the discovery of electrons, these electrons were termed as photoelectrons. The phenomenon is called photoelectric effect.
- The number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.
Einstein’s Photoelectric Equation: Energy Quantum of Radiation
- According to Einstien: Radiation energy is built up of discrete units – the so called quanta of energy of radiation. Each quantum of radiant energy has energy hν, where h is Planck’s constant and ν the frequency of light.
- Kmax = hν – φ0 , where φ0 is the work function of the metal
- E = hν where E = photon energy, h = planck constant and ν =frequency of wave
- p = h ν/c where p = momentum and c = speed of light
Wave Nature Of Matter
where p = momentum, K = kinetic energy, V = potential, mass = m, charge = e
where Δx = uncertainty in position and Δp = uncertainty in momentum