Aparticle of unit mass moves in a potential v(x)= ax^2+b/x^2 . where a and b are constnts. calcuate the angular frequency of small oscillations about the minimum of potential.

Explanation:

Given

Potential Energy is given by

And Force is given by

Particle will be at equilibrium when Potential Energy is either minimum or maximum

i.e.

So angular Frequency of small oscillation is given by

for

we get    

in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.

wind moving at higher speeds will transfer more energy to the water, resulting in stronger waves.