3. Consider the mass-spring system modeled as: dx dt m We let X = B 2m'...

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3. Consider the mass-spring system modeled as: dx dt m We let X = B 2m' -kx B x" +2\x' +wx: and w = y for our differential equation. Let's 1 > w. (a) Find the solution to the differential equation. Your result should be in terms of and w. (b) Suppose x (0) = 0, and x' (0) = vo > 0. Determine the solution to this initial value problem. 3. Suppose vo 0 1.0 0.8 (c) Let xo 1 - w 1, = 5, and w = 4. Let a = when x = 0, expressing t in terms of vo. 0.6 0.4 We have examined an overdamped mass-spring, and determined the minimum velocity for a return time to x = 0. 0.2 dx dt 0.0 = -0.2 x = 0 -0.4 k m' as in the text. Then we obtain suppose 0.1 0.2 0.3 0.4 Blue: Vo = 0.5 0.6 0.7 0.8 0.9 1.0 X -12, Green: vo -8, Red: vo = -4 3. Consider the mass-spring system modeled as: dx dt m We let X = B 2m' -kx B x" +2\x' +wx: and w = y for our differential equation. Let's 1 > w. (a) Find the solution to the differential equation. Your result should be in terms of and w. (b) Suppose x (0) = 0, and x' (0) = vo > 0. Determine the solution to this initial value problem. 3. Suppose vo 0 1.0 0.8 (c) Let xo 1 - w 1, = 5, and w = 4. Let a = when x = 0, expressing t in terms of vo. 0.6 0.4 We have examined an overdamped mass-spring, and determined the minimum velocity for a return time to x = 0. 0.2 dx dt 0.0 = -0.2 x = 0 -0.4 k m' as in the text. Then we obtain suppose 0.1 0.2 0.3 0.4 Blue: Vo = 0.5 0.6 0.7 0.8 0.9 1.0 X -12, Green: vo -8, Red: vo = -4