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 5 ft/s, and the subsequent motion takes place in a medium that offers a damping force numerically equal to two times the instantaneous velocity.
(a) Find the equation of motion if the mass is driven by an
external force equal to/(t) = 12 cos 2t + 3 sin 2t.
(b) Graph the transient and steady-state solutions on the same
(c) Graph the equation of motion.
solve the given differential equation by undetermined coefficients
y” – 4y = (x2 – 3) sin 2x
y”” – y” = 4x + 2xe-x
solve each differential equation by variation of parameters.
y” -y = sinh2x
solve the given initial-value problem. Use a graphing utility to graph the solution curve.
x2y” – 3xy’ + 4y = 0, y(l) = S, y'(l) = 3
Use the information given in the FIGURE to construct a mathematical model for the number of pounds of salt x1 (t), x2(t), and x3(t) at time t in tanks A, B, and C, respectively.
I’VE ATTACHED THE FIGURE.