1. a) Write the differential equations for the system below. Solve the equations for ‘x’ assuming that the system is at rest and undeflected before t=0. Also assume that gravity is present.
b) State whether the system is first or second order. If the system if first order find the time constant. If it is second order find the natural frequency and damping ratio.
2. a) Given the following differential equation and initial conditions, draw a sketch of the first 5 seconds. The input is a step function that turns on at t=0.
b) Solve the same problem as in part a) using explicit integration to get an equation that is a function of time.