Consider a particle that experiences the following two-dimensional acceleration: * = -kx = -2ky Find and sketch the path the particle takes by following the plan given below. Remember: the dot notation represents derivatives with respect to time. Plan: 1. Write each differential equation in the form: s+as+bs + c = 0. Which of the coefficients are zero? 2. Write down the characteristic equations for each differential equation. Remember: the characteristic equation takes the form: cr + cr + coro = 0. 3. Find the roots for each of your characteristic equations. 4. Use the roots to find the solution to each differential equation. 5. Use these initial conditions: at t = 0, (x,y) = (a,0) and x, y) = (0, yo) to find the constants of integration. 6. Use the result to sketch the path.