The damping term is nonlinear and represents air damping with a = 2 n/(m/sec)2 . the spring is a cubic spring and also is nonlinear with b = 5 n/m3 . the initial conditions are x(0) = 1 m and x . (0) = 0.5 m/sec. use a numerical method (e. g. euler’s method) to solve for displacement ""x"" and for velocity ""v"" for the following systems: part a) for a similar linear mass-spring-damper system (8 seconds of response) m x .. + ax . + bx = 0 part b) for a similar mass-spring-damper system with only the nonlinear spring term (8 seconds of response) m x .. + ax . + bx 3 = 0 part c) for a similar mass-spring-damper system with only the nonlinear damping term (80 seconds of response) m x .. + a|x . |x . + bx = 0 part d) for a the original mass-spring-damper system with both nonlinear terms (80 seconds of response) m x .. +

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