Question

Q3. (20') The motion of a spring-mass-damper system satisfies the initial value problem: m rac{d^2x}{dt^2} + b rac{dx}{dt} + kx = F, ?? x(0) = 0; ?(0) = 1 Given m = 1 kg, b = 5 Ns/m, k = 4 N/m, and F = 5 N. (a). What is the natural frequency of the system? (b). Is this system under damping or critical damping or over damping? Explain it. (c). Solve the given initial value problem. (d). The location of poles of X(s) affects the behavior of the system. How to choose parameters b/m and k/m so that the poles are placed at -4±4j?

          Q3. (20') The motion of a spring-mass-damper system satisfies the initial value problem:
m rac{d^2x}{dt^2} + b rac{dx}{dt} + kx = F, ?? x(0) = 0; ?(0) = 1
Given m = 1 kg, b = 5 Ns/m, k = 4 N/m, and F = 5 N.
(a). What is the natural frequency of the system?
(b). Is this system under damping or critical damping or over damping? Explain it.
(c). Solve the given initial value problem.
(d). The location of poles of X(s) affects the behavior of the system. How to choose parameters b/m and k/m so that the poles are placed at -4±4j?

Q3. (20') The motion of a spring-mass-damper system satisfies the initial value problem:
m racd^2xdt^2 + b racdxdt + kx = F, ?? x(0) = 0; ?(0) = 1
Given m = 1 kg, b = 5 Ns/m, k = 4 N/m, and F = 5 N.
(a). What is the natural frequency of the system?
(b). Is this system under damping or critical damping or over damping? Explain it.
(c). Solve the given initial value problem.
(d). The location of poles of X(s) affects the behavior of the system. How to choose parameters b/m and k/m so that the poles are placed at -4±4j?

Added by James S.

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