The equation of motion of a particle executing simple harmonic motion is given by x=3 (6 t+ 6 ) , where x is in metres and t is in seconds. The ratio of the potential and kinetic energies of the particle at time t=0 is

Step-by-step solution

Equation of motion is given as x=3 (6 t+ 6 ), A=3 At time t =0x=3 ( 6 )= 3 2 =1.5 Potential Energy of SHM is given as: V = 1 2 kx ^2 (1) Kinetic Energy of SHM is given as: K= 1 2 K (A^2-x^2 ) ...(2) Dividing Equation (1) and (2) aligned & V K = 1 2 K x^2 K (A^2-x^2 ) 2 & = x^2 A^2-x^2 aligned Substitute, x=1.5 and A=3 aligned & V K = (1.5)^2 (3)^2-(1.5)^2 = 2.25 9-2.25 & = 225 675 = 45 135 = 9 27 = 1 3 & V K = 1 3 aligned