2. Consider an unforced spring-mass system whose displacement is modelled by the ODE mx(t)" + cx'(t) + k x(t) = 0, with t in seconds, m = 2 kilograms, k = 5 newtons per meter, and c in N. sec per...

Extracted text: 2. Consider an unforced spring-mass system whose displacement is modelled by the ODE mx(t)" + cx'(t) + k x(t) = 0, with t in seconds, m = 2 kilograms, k = 5 newtons per meter, and c in N. sec per meter. a) What is the natural frequency of this system, in hertz? b) Find the value of c for critical damping. c) Find the value of c for which the system would oscillate with pseudo-frequency 0.25 hertz. Give the general solution in this case.