The city of Ann Arbor hires you to determine the dynamic properties of a frame system for which it has lost the original blueprints. Being a brilliant alumnus, you decide to do a free vibration test of the frame system. Supplied with a hydraulic jack, you are able to supply a jacking force to displace the frame. With a jacking force of 20 kips you note the frame has displaced 0.2 in. After jacking the frame, you release the frame from the jack and you record its motion. On the first return swing after release, the frame does not come back to the release point but rather only 0.16 in towards it. You recorded the time between the time of release, and the first return of 0.16 in- this time is 1.4 seconds. u(t). Jacking Force P m Determine the following: a. Natural frequency (wn) b. Mass of the girder (m) c. Logarithmic decrement (6) d. Damping ration (<) e. Damping coefficient (c) f. Damping frequency (wa) g. Amplitude of the frame after 6 cycles, u6 h. Plot the time history response of the system, u(t) 0