The equation of a simple harmonic motion of an oscillator is given by mx + kx...

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The equation of a simple harmonic motion of an oscillator is given by mx + kx = 0 where m is the mass, k is restoring force constant, * is the acceleration and x is displacement of the system. Show that the general solution for the displacement is: x = a sin (wt + p) where a is the amplitude, w is the angular frequency, t is time and is the phase of motion. (i) The total energy of the oscillator is given by E = ½mx² ½mx² + ½kx². Show that at any instant of time or displacement: E = mw²a² = ½ka². (ii) Sketch the graph of variation of potential energy and kinetic energy with displacement of an oscillator in simple harmonic motion. The equation of a simple harmonic motion of an oscillator is given by mx + kx = 0 where m is the mass, k is restoring force constant, * is the acceleration and x is displacement of the system. Show that the general solution for the displacement is: x = a sin (wt + p) where a is the amplitude, w is the angular frequency, t is time and is the phase of motion. (i) The total energy of the oscillator is given by E = ½mx² ½mx² + ½kx². Show that at any instant of time or displacement: E = mw²a² = ½ka². (ii) Sketch the graph of variation of potential energy and kinetic energy with displacement of an oscillator in simple harmonic motion.