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    ilovemath's Avatar
    ilovemath Posts: 6, Reputation: 1
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    #1

    Apr 20, 2012, 05:50 PM
    Differential Equations, Linear models
    A force of 64 N stretches a spring 4 meters. The mass of 4 kg is attached to the spring and set into motion in a medium that offer a damped force equal 16 times the velocity .If the mass is pulled down 2 centimeters from the equilibrium position and released. Find the equation for the position. Find the time(s) at which the mass passes the equilibrium position.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Apr 20, 2012, 06:13 PM
    The basic differenjtial equation for a mass, spring and damper is



    You know that k = 64N/4m = 16t N/m and C = 16N/(m/s). Set and solve for A and b. You should end up with a solution for b using the quadratic equation along the lines of


    Recall that if b is a complex number then the angular velocity is the imaginary part of the value for b and the damping constant is the real part. The value for A comes from the initial condition that x(0) = 0.02m. If you need more help post back with your work and we can help you along.

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