I need help with my practice project, I have done them I just need to cross reference your work with. mine, thanks so much!

1. Assuming that both springs have spring constant k and that there is a damping force proportional to velocity x' with damping constant y, write down the differential equation that describes the motion of the mass. Note that the expression for the force function depends on which of the three different parts of its domain x lies within. 2. The Heaviside, or unit step function, is dened by l, x Z c u(x c) = Qx 0, nd the crit- ical points of the differential equation in Problem 2 and dis- cuss their stability properties. 5. Consider the case of an undamped problem (y = 0) using the parameter values L = 1, m = 1, k = 1 and initial condi- tions x(0) = 2, x' (0) = 0. Find the solution x(t) of the initial value problem for 0 g t g f; and fl\" g t oo depend on the initial conditions. (c) Draw a phase portrait for the equivalent dynamical sys- tern. 7. Describe some other physical problems that could be for- mulated as event problems in differential equations