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In Sl units, the position x of a spring-loaded electromagnetic valve varies over timet in the manner described by the 2nd order ODE * + ax +(B + K)x = K The term on the RHS is designed so that, if x is disturbed from its rest position, then it automatically returns, ideally, after a short period of time with no overshoot. When a = 1,B = 1 and K = 1 the rest position of the system is x = 4' 5 a) Suppose that this system is at rest for the period 0

In Sl units, the position x of a spring-loaded electromagnetic valve varies over timet in the manner described by the 2nd order ODE * + ax +(B + K)x = K The term on the RHS is designed so that, if x is disturbed from its rest position, then it automatically returns, ideally, after a short period of time with no overshoot. When a = 1,B = 1 and K = 1 the rest position of the system is x = 4' 5 a) Suppose that this system is at rest for the period 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In Sl units, the position x of a spring-loaded electromagnetic valve varies over timet in the manner described by the 2nd order ODE * + ax +(B+ K)x = K The term on the RHS is designed so that, if x is disturbed from its rest position, then it automatically returns, ideally, after a short period of time with no overshoot. 1 the rest position of the system is x = When a = 1, B= 1 and K = 4' a) Suppose that this system is at rest for the period 0 < t < 3, but at t = 3 the system is disturbed. Solve the ODE 'by hand' with initial conditions x(3)= and x(3)= 2; and
Transcribed Image Text:In Sl units, the position x of a spring-loaded electromagnetic valve varies over timet in the manner described by the 2nd order ODE * + ax +(B+ K)x = K The term on the RHS is designed so that, if x is disturbed from its rest position, then it automatically returns, ideally, after a short period of time with no overshoot. 1 the rest position of the system is x = When a = 1, B= 1 and K = 4' a) Suppose that this system is at rest for the period 0 < t < 3, but at t = 3 the system is disturbed. Solve the ODE 'by hand' with initial conditions x(3)= and x(3)= 2; and
b) It is suggested that using a system with a = 8, B = 16 and K = 4 would return to its rest position 1 of in a more desirable way. Use MATLAB (include a screenshot) to solve this new ODE with initial conditions x(3)= and *(3)= 2, 115
Transcribed Image Text:b) It is suggested that using a system with a = 8, B = 16 and K = 4 would return to its rest position 1 of in a more desirable way. Use MATLAB (include a screenshot) to solve this new ODE with initial conditions x(3)= and *(3)= 2, 115
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