Weight And Springs

In the \(xyz\)-coordinate system, there are 4 fixed (immovable) points at \[(x,y,z) = (\SI{1}{\meter},\SI{0}{\meter},\SI{0}{\meter}),\ (\SI{0}{\meter},\SI{1}{\meter},\SI{0}{\meter}),\ (\SI{-1}{\meter},\SI{0}{\meter},\SI{0}{\meter}),\ (\SI{0}{\meter},\SI{-1}{\meter},\SI{0}{\meter}).\] There is a movable \(\SI{1}{\kilo \gram}\) mass attached to each of the 4 fixed points by a spring of spring constant \(k = \SI{1}{\newton \per \meter}\). The mass is initially at rest at \((x,y,z) = (\SI{0}{\meter},\SI{0}{\meter},\SI{0}{\meter})\), and the springs are initially un-stretched.

The mass falls under the influence of gravity \(\big(\SI{10}{\meter \per \square \second}\big)\) in the \(-z\) direction of the springs. When air resistance eventually brings the mass to rest at an equilibrium position, how far (in meters) is the mass from the origin (to 2 decimal places)?

Note: All quantities are in standard SI units.

×

Problem Loading...

Note Loading...

Set Loading...