Consider a block of mass m that is initially at rest on an inclined plane at an angle β from the horizontal. the block is acted on by an applied force f(t) directed up the plane. the plane is lubricated with a viscous oil of effective damping constant b. the applied force is a 400 n step applied at t = 0. if m = 80 kg, b = 12 n*s/m, and β = 20°, do the following:

a. calculate (analytically) the steady-state speed of the block.

b. find (analytically) the time constant of the system.

c. calculate (analytically) approximately how long it takes for the block to reach its steadystate speed.

d. write an analytical expression for the speed as a function of time