Consider the following initial value problem for a spring-mass-dashpot system:4x" + 16х' + kx — 0,x(0) — —1.5, х'(0) — 8a) Find the value of the spring constant k that makes the spring critically damped.b) If k = 116, write the solution x(t) in the form Ce¬pt cos(wit – a1).|

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Consider the following initial value problem for a spring-mass-dashpot system: 4x" + 16x' + kx = 0, x(0) = –1.5, x'(0) = 8 a) Find the value of the spring constant k that makes the spring critically damped. b) If k = 116, write the solution x(t) in the form Ce¯pt cos(w¡t – a1).

Consider the following initial value problem for a spring-mass-dashpot system: 4x" + 16x' + kx = 0, x(0) = –1.5, x'(0) = 8 a) Find the value of the spring constant k that makes the spring critically damped. b) If k = 116, write the solution x(t) in the form Ce¯pt cos(w¡t – a1).

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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Consider the following initial value problem for a spring-mass-dashpot system:
4x" + 16х' + kx — 0,
x(0) — —1.5, х'(0) — 8
a) Find the value of the spring constant k that makes the spring critically damped.
b) If k = 116, write the solution x(t) in the form Ce¬pt cos(wit – a1).
|

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