Answer to Question #318033 in Classical Mechanics for Johannes Steven

Question

A spring with mass of 2 kg has natural length of 0.5 m. A force of 25.6 N is required to maintain, it stretched to a length of 0.70 m. If the string is stretching to a length of 0.70 m and then released with initial velocity 0, find the position of mass at anytime t.

Answer 1

$k=\frac Fl=51.2~\frac Nm,$

$B=l'-l=0.2~m,$

$\omega=\sqrt{\frac km}=5 .1~\frac{rad}s,$

$x=0.5+0.2\cos 5.1t.$