Problem $1$: In this problem, you will develop the deformation response spectrum for

the following earthquake acceleration time history from the $1994$

Northridge earthquake. You have been provided the time history in digital

format $($TimeHistory$\_$HW#$5.$xls$).$

Develop the response spectrum at damping ratio $=5\%$ using the

following steps $($provide the calculations for one natural period $$ please

upload the file showing the calculations as well$)$:

$1.$ Compute the maximum relative deformation at twenty natural periods

at intervals of $0\mathrm{.}05$ sec starting at $0\mathrm{.}05$ sec$.$

$2.$ Use the method based on interpolation of excitation with coefficients

given in Table $5\mathrm{.}2\mathrm{.}1.$

$3.$ Also use the linear acceleration method and compare the results to

that obtained in Step $(2)$

$4.$ Plot the maximum deformation versus the natural period and also

provide in tabular form.

$($Hint: Assume the mass of the SDOF system is unity and compute the

stiffness for the desired natural period$).$