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Unformatted text preview: 18.03: Differential Equations, Spring, 2006 Driving through the dashpot The Mathlet Amplitude and Phase: Second order considers a spring/mass/dashpot system driven through the spring. If y ( t ) denotes the displacement of the plunger at the top of the spring, and x ( t ) denotes the position of the mass, arranged so that x = y when the spring is at rest, then we found the second order LTI equation m ¨ x + bx ˙ + kx = ky . Now suppose instead that we fix the top of the spring and drive the system by moving the bottom of the dashpot instead. Here’s a frequency response analysis of this problem. This time I’ll keep m around, instead of setting it equal to 1 or dividing through by it. A new Mathlet, Amplitude and Phase: Second Order, II , illustrates this system with m = 1. Suppose that the position of the bottom of the dashpot is given by y ( t ), and again the mass is at x ( t ), now arranged so that x = 0 when the spring is relaxed. Then the force on the mass is given by d x m ¨ =...
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This note was uploaded on 01/31/2011 for the course MAT 17A taught by Professor Staff during the Winter '08 term at UC Davis.
- Winter '08