3.) (1 point) If 5y+10y+Cy=0 models a particular system, determine the value of C that creates a double root when solving the characteristic equation. Solve the resulting second order homogeneous linear ODE if y(0)=14 and y()=0. 4.) (1 point) A model for damped motion is: mx+bx+kx=0 For this type of system, someone (a seagull) can set the initial condition by physically moving a mass, m, attached to a spring ( k ) and dashpot (b) to store some potential energy in the spring. Once the mass is released, the system will dissipate energy through the dashpot until the mass comes to rest. For many physical systems, oscillations are undesirable, so they are engineered to be overdamped. (Solutions to the ODE will not contain sines/cosines). - For a physical system, x will represent position (in meters), m is mass (kg) and k is the spring constant (N/m). Analyze the Characteristic Equation of the model and show the appropriate value for b such that the system will be overdamped (in terms of m and k ). - What are the units of b (in this case)? - Does increasing the damping of a system help to mitigate unwanted oscillations