The displacement of two identical particles performing S.H.M are represented by equation x₁ = 6 ( 5t + /4) and x₂ = 4 t . The energies of both the particles will be same, if the value of is

Step-by-step solution

The total energy of a particle performing simple harmonic motion is given by E = 1 2 m ^2 A^2 For the first particle, the amplitude is A₁ = 6 and the angular frequency is ₁ = 5 . Its energy is E₁ = 1 2 m (5)^2 (6)^2 = 1 2 m (25)(36) = 450 m For the second particle, the amplitude is A₂ = 4 and the angular frequency is ₂ = . Its energy is E₂ = 1 2 m ( )^2 (4)^2 = 8 m ^2 Since the particles are identical, their masses are the same. Given that their energies are equal, we have E₁ = E₂ 450 m = 8 m ^2 ^2 = 450 8 = 225 4