Question

A ball weighing 1kg, suspended on a spring, oscillates harmoniously with an amplitude of 10 cm and a period T = 3s. Determine the kinetic energy when the ball is in equilibrium

Answer 1

$\text{according to the law of conservation of energy:}$

$E_k+E_p= const$

$E_p=\frac{kx^2}{2}$

$x\text{ is the distance from the equilibrium point}$

$T=2\pi\sqrt{\frac{m}{k}}$

$k=(\frac{2\pi}{T})^2m=(\frac{2\pi}{3})^2*1\approx2.09$

$E{p}\text{ maximum if }x=0.1$

$E_{pmax}=\frac{kx^2}{2}=\frac{2.09*0.1^2}{2}=0.01$

$\text{if }x=0\ E{kmax}=E_{pmax}$

$E_k(0) = 0.01J$

Answer: 0.01 J kinetic energy when the ball is in equilibrium