MA 2051 D '97 Sample Exam 2
- Consider the following differential equation, describing a
damped spring-mass system.
- Find the roots of the characteristic equation. Classify
the spring-mass system
as underdamped, overdamped, or critically damped.
- Find two linearly independent solutions to the
differential equation. Use the Wronskian to prove that your solutions
really are linearly independent.
- Find the solution that satisfies the initial conditions
x(0)=-2, x'(0) = 4.
- Consider the forced, undamped spring-mass differential equation shown
- Find the general solution of the homogeneous differential equation.
- Find a particular solution.
- Find the general solution that satisfies the initial conditions
x(0)=1 and x'(0)=-2.
- Consider the following system of differential equations.
- Find the characteristic equation and determine its roots.
- Find the two linearly independent solutions. (You need
not verify that they are linearly independent.)
- Find the solution that satisifies the initial condition
- Sketch the phase portrait for this system over the region , . Include at least four trajectories in
- On the direction field given below, sketch trajectories starting
at the initial conditions x(0)=-1, y(0)=0.5 and x=1.5,