Answer to Question #173133 in Classical Mechanics for Gergana

Question

A ball with mass 1kg suspended on a spring oscillates nutritionally with the amplitude A = 10cm and period T = 3s.Determine the kinetic and potential energy of the ball when it is deviated from the equilibrium position at a distance x = A/2

Answer 1

$$E=0.5mv^2=0.5m\omega^2A^2\\E=m\frac{4\pi^2}{T^2}A^2\\E=1\frac{4\pi^2}{3^2}0.1^2=0.0439\ J$$

$$\\K=1\frac{4\pi^2}{3^2}0.05^2=0.0110\ J\\U=0.0439-0.011=0.0329\ J$$