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4. Consider a spring-mass-damper system with mass m, spring constant k and damping coef- ficient 7. The differential equation describing the motion of the mass is d²x dx m +y + kx = 0 dt² dt where x denotes the displacement of the mass from its rest position and t denotes the time variable. Given m = 1 kg, y = 1 Ns/m and k = 9.25 N/m, x(0) = 9.25 N/m, x(0) = 2 m and x'(0) = 8 m/s,

(a) determine the maximum displacement of the mass from its rest position for t≥ 0; [5 marks] (b) within 5 s starting from t = 0, how many times does the mass cross its rest position? [2 marks]