8.A certain vibrating system satisfies the equation u″ + γu′ + u = 0. Find the value of the damping coefficient γ for which the quasi-period of the damped motion is 50% greater than the period of the corresponding undamped motion.

Answer both questions please

2.5 Consider the system x' = (² 9) x. Find the special values of a for which the phase plane changes type. (Assume det A=0).

(a) Write down the equation of motion for the point particle of mass m moving in the Kepler potential U(x) = -A/x+ B/x² where x is the particle displacement in m. (d) Mimimise the number of independent parameters in the modified equation of motion with dissipation by introducing dimensionless varibles and r for x and r. (e) Present the equation derived in the form of an energy balance equation and find the expressions for the effective kinetic and potential energies (7 and V), and dissipative function F.