For each nonlinear equation of motion, linearize the equation and discuss the range of validity of the linearized equation. (For example: the linearized equation of motion has an x% error in the...

For each nonlinear equation of motion, linearize the equation and discuss the range of validity of the linearized equation. (For example: the linearized equation of motion has an x% error in the nonlinear term cos  for  > 0.) Analytically solve the linearized equations of motion and numerically solve the fully nonlinear equation using a program such as MATLAB.35 Plot the linear and nonlinear timehistories on the same graph and discuss the comparisons.

(a)  + 3 cos  = 0; (0) = 0:5; _(0) = 0 (b)  + 3 sin  = 0; (0) = 0:5; _(0) = 0 (c)  + 3 cos2  = 0; (0) = 0:5; _(0) = 0 (d)  + 3 sin2  = 0; (0) = 0:5; _(0) = 0: