{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture_29 (dragged)

lecture_29 (dragged) - MA 36600 LECTURE NOTES MONDAY APRIL...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MA 36600 LECTURE NOTES: MONDAY, APRIL 6 Applications Spring-Mass System: One Mass, Two Springs. Now say that we have a mass m attached to two springs with constants k 1 and k 2 , respectively. We assume that these springs are attached to the opposite ends of a track of fixed length , with the mass m in between. We continue to assume that the mass is under the influence of an external force F ( t ). Denote x = x ( t ) as the displacement from equilibrium on the track at time t . We seek a di ff erential equation for x . Let L 1 and L 2 denote the lengths to which the first and second springs are stretched at equilibrium, respectively. Using Hooke’s Law, we see that the force exerted on the mass from the first spring is k 1 L 1 (pulling to the left), whereas the force exerted on the mass from the second spring is + k 2 L 2 (pulling to the right). Since we are at equilibrium, the sum of the forces must be zero: k 1 L 1 + k 2 L 2 = 0 L 1 + L 2 = = L 1 = k 2 k 1 + k 2 , L 2 = k 1 k 1 + k 2 .
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online