Question: Using Newton's second law model for a vibrating spring with damping and no forcing, my'' + by' +ky =0, find the equation of motion if

Using Newton's second law model for a vibrating spring with damping and no forcing, my'' + by' +ky =0, find the equation of motion if m=10kg, b = 60kg/sec, k=250kg/sec², y(0)=0.3, and Y'(0) = -0.1 m/sec. What is the position of the mass after 1 second? Show all work.

I did all appropriate substitution and came to the polynomial 10r^2 + 60r + 250 = 0. Without using imaginary numbers, this is a false argument. And I do not know how to do it with imaginary numbers.

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