$($a$)$ Static and dynamic analyses are types of analysis that are often carried out in obtaining the performance of a structure.

$($i$)$ Discuss in detail the meaning of static and dynamic analyses and

discuss how it is possible to differentiate between the two analyses.

$($ii$)$ With appropriate sketches, discuss briefly two $(2)$ types of dynamic

testing that are commonly conducted in the field or laboratory.

$(16$ marks$)$

$($b$)$ Figure Q$3$ illustrates a concrete portal frame with rigid floors. Properties of the

portal frame are provided as follow.

Mass, $m_1=1000kg$ and $m_2=800kg$

Elastic modulus, $E=24k\frac{N}{m}{m}^2$

Figure Q$3$

Determine the following information of the frame.

$($i$)$ Modal frequencies $({}_1,{}_2)$

$($ii$)$ Mode shape vectors $({}_1,{}_2)$