Reading Recommendations:

$$ Lecture Notes

$$ Chopra, A$.,$ Dynamics of Structures: Theory and Applications to Earthquake Engineering, Prentice Hall.

An SDOF system has the following properties: $m=45,594kg,k=18k\frac{N}{c}m,T_n=1s(w_n=6\mathrm{.}283$ of the system to $p(t)$ defined by the half$-$ rad$/$s$)$ and $=0\mathrm{.}05.$ Determine the response $u(t)$ cycle sine pulse force shown in figure by;

a$.$ Using piecewise linear interpolation of $p(t)$ with $t=0\mathrm{.}1s$ and

b$.$ Evaluating the theoretical solution

Solve Problem$\_1$ by 'Central Difference Method' using $t=0\mathrm{.}1s.$

Solve Problem$\_1$ by 'Newmark's Method' applying both the constant average acceleration and linear acceleration procedures using $t=0\mathrm{.}1s.$

Compare the solutions on a diagram with the theoretical solution and give brief information about the methods.