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critically damped mass-spring-dashpot system with position x(t) satisfies the ODE below with given initial position and velocity, in which positive values of x mean the spring is stretched and negative values mean the spring is compressed. x"+4x+4x= 0, x(0) = 1, x'(0) = vo (where vo is a constant) a) Find the position x(t) for all t > 0 in terms of vo Answer: b) For what value(s) of vo (if any) does the mass pass through equilibrium? Answer: c) Now suppose that vo = 10, how long does it take for the spring to become maximally stretched? Answer:

critically damped mass-spring-dashpot system with position x(t) satisfies the ODE below with given initial position and velocity, in which positive values of x mean the spring is stretched and negative values mean the spring is compressed. x"+4x+4x= 0, x(0) = 1, x'(0) = vo (where vo is a constant) a) Find the position x(t) for all t > 0 in terms of vo Answer: b) For what value(s) of vo (if any) does the mass pass through equilibrium? Answer: c) Now suppose that vo = 10, how long does it take for the spring to become maximally stretched? Answer:

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.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 15E
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critically damped mass-spring-dashpot system with position x(t) satisfies the ODE below with given initial position and velocity, in which positive values of x mean the spring is stretched and negative values mean the spring is compressed. x" +4x+4x = 0, x(0) = 1, x'(0) = vo (where vo is a constant) a) Find the position x(t) for all t > 0 in terms of vo Answer: b) For what value(s) of vo (if any) does the mass pass through equilibrium? Answer: c) Now suppose that vo = 10, how long does it take for the spring to become maximally stretched? Answer:
Transcribed Image Text:critically damped mass-spring-dashpot system with position x(t) satisfies the ODE below with given initial position and velocity, in which positive values of x mean the spring is stretched and negative values mean the spring is compressed. x" +4x+4x = 0, x(0) = 1, x'(0) = vo (where vo is a constant) a) Find the position x(t) for all t > 0 in terms of vo Answer: b) For what value(s) of vo (if any) does the mass pass through equilibrium? Answer: c) Now suppose that vo = 10, how long does it take for the spring to become maximally stretched? Answer:
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ISBN:
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