Solve Problem 13.48 using a forcing frequency \(\omega=10 \mathrm{rad} / \mathrm{s}\) instead of \(5 \mathrm{rad} / \mathrm{s}\).

Data From Problem 13.48:-

A single-degree-of-freedom system has a softening spring and is subjected to a harmonic force with the equation of motion given by

Find the response of the system numerically using the fourth-order Runge-Kutta method for the following data for two cases-one by neglecting the nonlinear spring term and the other by including it:
\[M=10 \mathrm{~kg}, \quad c=15 \mathrm{~N}-\mathrm{s} / \mathrm{m}, \quad k_{1}=1000 \mathrm{~N} / \mathrm{m}, \quad k_{2}=250 \mathrm{~N} / \mathrm{m}^{3}, \quad \omega=5 \mathrm{rad} / \mathrm{s}\]
Compare the two solutions and indicate your observations.

mxcxkx k2x - = A cos wt (E.1)