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Part 1 [ 4 0 % ] : Accuracy and stability analysis of Newmark's method For a given undamped free vibration dynamic system u +

Part 1[40%]: Accuracy and stability analysis of Newmark's method
For a given undamped free vibration dynamic system u+2u=0 with a zero initial
displacement and a nonzero initial velocity u(0)=u0(choose any values for and u0),
assess the accuracy of the algorithm by plotting the error of the computed period for a
wide range of different time steps.
The stability of the algorithm is accessed by following the procedure: 1) choose a time
step; 2) record the maximum kinetic energy of the system over a time integration interval
of 0,100T, where T is the natural period of the system; and 3) if a significant increase of
the energy is observed, it would indicate that the algorithm is unstable for the
corresponding and larger time steps. The procedure should be repeated for a large range
of different time steps. MATLAB program for this question
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