pre algebra

A 0.25 kg mass is horizontally attached to a spring with a stiffness 4 N/m. The damping
constant b for the system is 1 N-sec/m. If the mass is displaced 0.5 m to the left and given an
initial velocity of 1 m/sec to the left, find the equation of motion. What is the maximum
displacement that the mass will attain?

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  1. Differential equations, initial value problem.

    The general equation of motion is:
    mx"+Bx'+kx=f(t), where the independent variable is t, and the displacement x is the dependent variable.

    In this case, external force f(t)=0, so
    we have a differential equation of motion with constant coefficients:
    Divide by the leading coefficient:
    Auxiliary equation:
    m1=-2+2√3, m2=-2-2√3
    α=-2, β=2√3
    So the solution for x is:
    Since x(0)=-0.5, we have
    or C1=-0.5

    x'(0)=-1 to get
    Therefore the equation of motion is:

    Check my arithmetic.

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