The position of a weight attached to a spring and a dashpot damping device is given by the function 2 x(t) = e-t (-2 cos 3t – sin 3t Where x(t), measured in feet, is the displacement from the...

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Extracted text: The position of a weight attached to a spring and a dashpot damping device is given by the function 2 x(t) = e-t (-2 cos 3t – sin 3t Where x(t), measured in feet, is the displacement from the equilibrium position of the spring system and t is measured in seconds (Figure 1). Find the initial position and the initial velocity of the weight. Hint: Initial condition is at t = 0. x =0 (equilibrium position) m Figure 1: The system in equilibrium (positive direction is downward)