Question

1.)
A particle is undergoing SHM, when its kinetic
energy is equal to potential energy, the velocity of
particle is (o - angular frequency, A - amplitude
and potential energy at mean position is zero)​

Answer 1

Explanation:

1/2K(A^2-x^2) = 1/2 kx^2

x = A/√2

v= o√A^2/2

Answer 2

The velocity of the particle is oA/√2 m/s

The kinetic energy of a particle in SHM = 1/2 k (A²-x²)

The Potential energy of the particle = 1/2 k x²

k is the force constant and x is the displacement of the particle from the mean position .

Given ,

Kinetic energy = Potential energy

=> 1/2 k(A²-x²) = 1/2 kx²

=> A² = 2x²

=> x = A/√2

Velocity of the particle at x = x × o

[o is the angular velocity]

Velocity of the particle = oA/√2 m/s