lecture_29 (dragged) - MA 36600 LECTURE NOTES: MONDAY,...

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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 Fxed length ° , with the mass m in between. We continue to assume that the mass is under the in±uence of an external force F ( t ). Denote x = x ( t ) as the displacement from equilibrium on the track at time t . We seek a di²erential equation for x . Let L 1 and L 2 denote the lengths to which the Frst and second springs are stretched at equilibrium, respectively. Using Hooke’s Law, we see that the force exerted on the mass from the Frst 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 °.
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue University-West Lafayette.

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