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

Question

The equation of motion of a particle executing simple harmonic motion is given by x=3 sin ⁡(6t+ 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

Accepted Answer

Correct answer: D. (d) Equation of motion is given as x=3 sin ⁡(6t+ 6) ,A=3 At time t=0 x=3 sin ⁡ ( 6 )= 32=1.5 Potential Energy of SHM is given as: V= 12kx^2……(i) Kinetic Energy of SHM is given as: K= 12K(A^2-x^2) … . . ( ii ) Dividing Equation (1) and (2) VK= 12 Kx^2K(A^2-x^2) 2= x^2A^2-x^2 Substitute, x=1.5 and A=3 VK= (1.5 )^2 (3 )^2- (1.5 )^2= 2.259-2.25= 225675= 45135= 927= 13 VK= 13

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

Solution

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