a$)$ How to differentiate between static and dynamic loading? Describe types of dynamic

loading. Explain D'Alembert's Principle.

b$)$ A SDOF system consists of the following parameters: mass, $m=5kg,k=100\frac{N}{m}$

and damping $e=3N-s\frac{ec}{m}.$ Determine:

$($i$)$ the damping factor

$($ii$)$ the natural frequency of the damped vibration

$($iii$)$ logarithmic decrement

$($iv$)$ No$.$ of cycles after which the original amplitude is reduced to $20\%?$

a$)$ Determine the response of the following system under the given initial conditions.

Stiffness $320k\frac{N}{c}m,$ weight $=58\mathrm{.}86kN,$ damping constant $=4,$ initial displacement $=$

$2cm$ and initial velocity $=7\mathrm{.}6\frac{m}{sec}.$ Also plot the response.

b$)$ For a SDOF system is subjected to a rectangular pulse load of amplitude $100KN$ and

duration $0\mathrm{.}4$ second. Determine the response of the tower having mass $500kg$ and

stiffness $200k\frac{N}{c}m$ during forced vibration and free vibration phase. Assume

undamped system.

a$)$ A steel rigid frame, as shown in figure below, supports a rotating machine, which

exerts a horizontal force at the girder level of $50,000sin11tN.$ Assuming $4$ percent

critical damping, what is the steady state amplitude of vibration? $I_{\text{c}\text{o}\text{l}\text{u}\text{m}\text{n}}=1500{10}^{-7}$

$m^4,E=21{10}^{10}\frac{N}{m^2}.$

b$)$ Explain with an example how Holzer's method is carried out to determine the first

mode of frequency of shear building.