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.2 Gun barrel. Solve y" + y = 1 – t2/T if 0S t=T and 0 if t→; here, y(0) = 0, y'(0) = 0. This models an undamped system on which a force F acts during some interval of time (see Fig. 59), for instance, the force on a gun barrel when a shell is fired, the barrel being braked by heavy springs (and then damped by a dashpot, which we disregard for simplicity). Hint: At T both y and y' must be continuous. m = 1 k = 1 F F = 1 - t/n2 1 F = 0

.2 Gun barrel. Solve y" + y = 1 – t2/T if 0S t=T and 0 if t→; here, y(0) = 0, y'(0) = 0. This models an undamped system on which a force F acts during some interval of time (see Fig. 59), for instance, the force on a gun barrel when a shell is fired, the barrel being braked by heavy springs (and then damped by a dashpot, which we disregard for simplicity). Hint: At T both y and y' must be continuous. m = 1 k = 1 F F = 1 - t/n2 1 F = 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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.2 Gun barrel. Solve y" + y = 1 – 12/1 if 0 = tS T and 0 if t→ o; here, y(0) = 0, y' (0) = 0. This models an undamped system on which a force F acts during some interval of time (see Fig. 59), for instance, the force on a gun barrel when a shell is fired, the barrel being braked by heavy springs (and then damped by a dashpot, which we disregard for simplicity). Hint: At T both y and y' must be continuous. t %3D - m = 1 k = 1 F F = 1 - t2/2 1 F = 0 TO
Transcribed Image Text:.2 Gun barrel. Solve y" + y = 1 – 12/1 if 0 = tS T and 0 if t→ o; here, y(0) = 0, y' (0) = 0. This models an undamped system on which a force F acts during some interval of time (see Fig. 59), for instance, the force on a gun barrel when a shell is fired, the barrel being braked by heavy springs (and then damped by a dashpot, which we disregard for simplicity). Hint: At T both y and y' must be continuous. t %3D - m = 1 k = 1 F F = 1 - t2/2 1 F = 0 TO
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