Consider the following model for a mechanical dynamic system consisting of a

two linear springs with stiffnesses 1417 N/m and a linear viscous damper with

damping 78 N-s/m that are connected between a rigid wall and a 13 kg moving

mass (frictionless rollers).

The initial position and velocity are zero. There is a nonzero input force.

F(t) ¼ 2834 u(t) N

Complete the following.

(a) Find the equation of motion and solve for x(t) using Laplace transforms

and check using the ilaplace command in MATLAB®.

(b) Calculate the natural frequency ωn, the damping ratio ζ, and the dominant

time constant for this system.

(c) Using the symbolic manipulation capability in MATLAB®, show that your

answer satisfies the initial conditions and solves the original equation of

motion.

(d) In MATLAB®, plot x(t) for a duration equal to four times the dominant time

constant.

Solution.pdf

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