In: Physics
A mass of 2 kilogram is attached to a spring whose constant is 8 N/m, and the entire system is then submerged in a liquid that imparts a damping force equal to 8 times the instantaneous velocity. At t = 0 the mass is released from the equilibrium position with no initial velocity. An external force f(t) = 2U(t−1)*e^(−2(t−1)) is applied.
(a) Write f(t), the external force, as a piecewise function and
sketch its graph.
(b) Write the initial-value problem.
(c) Solve the initial-value problem.
(d) What type of motion does the solution of the initial value
problem describe? (forced undamped motion, forced overdamped
motion, forced critically damped motion, or forced underdamped
(oscillatory) motion)