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:
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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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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