A $12-$ft$-$long vertical cantilever, a $8-$in$.-$nominal$-$diameter standard

steel pipe, supports a $5200-lb$ weight attached at the tip as shown in

the Figure. The properties of the pipe are: second moment of cross$-$

sectional area, $I=72\mathrm{.}5i{n}^4,$ elastic modulus $E=29,000$ksi, and the

total weight of the pipe can be neglected. Assume the damping ratio

of the system is $2\%.(1)$ Plot the responses of relative displacement

and absolute acceleration of the weight due to the $1940El$ Centro

earthquake NS ground motion. $(2)$ Determine the maximum relative

displacement, $(u_i{)}_{\text{m}\text{a}\text{x}},$ and absolute acceleration, $u_{i,\text{m}\text{a}\text{x}}^t.$ Solve this

problem by linear acceleration of Newmark's method with $t=0\mathrm{.}02$

sec$.$