A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is at

Question

A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion. x(t) = m A mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Initially, the mass is released 1 foot below the equilibrium position with a downward velocity of 9 ft/s, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. (a) Find the equation of motion if the mass is driven by an external force equal to f(t) = 20 cos 2t + 5 sin 21. x(t) = Solve the given initial-value problem. D^2x dt^2 + 4x = -6 sin 2t + 3 cos 2t, x(0) = -1, x'(0) = 1 X(t) = -cos(2t) - sin(2t) / 3 + 2t cos(2t) + tsin()2t_ 3 Solve the given initial-value problem. xy"+y'=x, y{ 1) = 3, y 1) = - 1 /2 y(x) =

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