Classical Mechanics (Kibble & Berkshire) · Problem 5.1

Energy conservation — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · free-linear-oscillations

Problem

A certain oscillator satisfies the equation x¨+4x=0.\ddot{x} + 4x = 0. Initially the particle is at the point x=3x = \sqrt{3} when it is projected towards the origin with speed 2. Show that, in the subsequent motion, x=3cos⁡2t−sin⁡2t.x = \sqrt{3}\cos 2t - \sin 2t. Deduce the amplitude of the oscillations. How long does it take for the particle to first reach the origin?

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