Q3 (i) The displacement x(t) of an unforced simple harmonic oscillator obeys the equation of motion i + 251 = 0. Show that the energy E = (12 + 2512) is a constant by differentiating this expression with respect to time and using the equation of motion. (ii) Initially at t = 0, the simple harmonic oscillator is undisturbed and at rest so that r(0) = (0) = 0. An external force is then applied during the time period 0