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National Bird Day: Why Birds Matter to Us

National Bird Day is celebrated every year on 5 January . This day is observed to spread awareness about birds, their importance in nature, and the need to protect them. Birds are beautiful living beings and play a very important role in keeping our environment healthy. Origin of National Bird Day National Bird Day was first celebrated in the year 2002 . It was started by bird lovers and environmental groups to protect birds from dangers like deforestation, pollution, and illegal hunting. The main aim of this day is to teach people, especially students, why birds are important and how we can help save them. Why Is National Bird Day Celebrated Every Year? National Bird Day is celebrated every year because many bird species are disappearing due to human activities. Cutting trees, using plastic, pollution, and climate change are harming birds and their homes. This day reminds us that: Birds need protection Nature should be respected Everyone has a responsibil...
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Concept of potential well | Oscillations and Waves

 Equilibrium and concept of potential well

  • In all conservative field, potential energy U = U (x, y, z)
  • Since force
                        
    • If particle moves only along x-axis, then force Fx = - (∂U/∂x)
    • Similarly Fy = - (∂U/∂y) and Fz = - (∂U/∂z)
    • Force = slope of tangent at any point of the curve
    • Since the tangent at P, Q, R and S are parallel to x-axis
      • These positions are known as equilibrium positions.
      • If a particle is slightly displaced from stable equilibrium position P, then it starts to oscillate between points A and B until it crosses point B.
      • P is the position having minimum potential energy and is called stable equilibrium.
      • The region of minimum potential energy bounded between points A and B is called  potential well .
      • The difference between the maximum and minimum potential energy of a potential well is called the  binding energy of potential well.
      • If the energy of particle is less than the B.E. of well, then it is always bound in the potential well and such state is called  bound state .
      • Let a particle be slightly displaced from its mean position P = (x = x0) then from Taylor sereis expansion, its potential energy at any point x
      • For stable equilibrium position P
      • If P lies at origin i.e., x0 = 0 and U(x0) = 0
      • For small displacement x3 → 0, x4 → 0, ...
                          
                              
            • In this position a curve between displacement and potential energy will be a  parabola and F ∝ x
            • Therefore the motion of particle in a parabolic potential well is always oscillatory and is simple harmonic .

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