Question If the soil exerts a trapezoidal distribution of load on the bottom of the footing, determine the intensities w1 and w2 of this distribution needed to support the column loadings. 80 kN60 kN50 kN1m-1m-25 m- 3.5 m-W2Prob. 4–149

(d) A 3 m high, 6 m wide rectangular gate is hinged at the top edge at A an is restrained by a fixed ridge at B as shown in Figure Q1(d). Calculate the hydrostatic force exerted on the gate by the 5 m high water and determine the location of the pressure center. 2 m Water A Gate 3 m B FIGURE Q1(d)

Assume that you measured the length of an object as 50 mm using a digital caliber. The measurement was made at 300 + 5 K. What is the actual measurement result? (Resolution of the digital caliber: 0.04 mm, coverage factor: 3, linear thermal expansion coefficients of the digital caliber and the sample are 14*10-6 KP)

Determine the reactions at the supports A and C. The frame is pin connected at A, B, and C and the two joints are fixed connected. SKN 6 kN 10 kN/m 2 kN/m B 4 m A 3 m -2 m -1 m -

The circuit below shows a filter commonly used as the output stage of a power supply. In this application, Vin(t) is switched between 0 and a DC input supply voltage (12V in this case). The filter smooths the switched input so that it is close some desired output from 0-12V. In this exercise, you are interested in determining the start-up behaviour of the system. To this end, do the following: a) Find the transfer function Vout(s) . You may assume that the capacitor and inductor are initially de- Vin(s) energised. b) Att = 0, Vin(t) is switched to 12 V (i.e. Vin(t) = 12u(t)). Find the time response Vout(t) = [-{Vout(s)}. Please use partial fraction expansion and the Laplace Transform table to conduct the inversion(s), showing all of your work and explaining your logic clearly to receive full credit. c) How long will it take for vout (t) to reach 6V? You may use computer tools here, but please clearly explain your logic for full credit. d) Sketch (by hand) the Bode plot for G(s) with the parameter values from part b. As a part of this, please carefully compute and label: i. All asymptotes (e.g. low-frequency & high frequency) All corner frequencies iii. The frequency and magnitude (in dB) of any resonances (if they exist) 50 x 10-3 H 000m 0.25 12 Vin(t) 0.2F 112 Vout(t) Figure 2: System for Question 3

The circuit below shows a filter commonly used as the output stage of a power supply. In this application, Vin(t) is switched between 0 and a DC input supply voltage (12V in this case). The filter smooths the switched input so that it is close some desired output from 0-12V. In this exercise, you are interested in determining the start-up behaviour of the system. To this end, do the following: a) Find the transfer function Your C). You may assume that the capacitor and inductor are initially de- Vin) energised. b) Att = 0, Vin(t) is switched to 12 V (i.e. Vin(t) = 12u(t) ). Find the time response Vout(t) = [-!{Vout($)}. Please use partial fraction expansion and the Laplace Transform table to conduct the inversion(s), showing all of your work and explaining your logic clearly to receive full credit. c) How long will it take for Vout(t) to reach 6V? You may use computer tools here, but please clearly explain your logic for full credit. d) Sketch (by hand) the Bode plot for G(s) with the parameter values from part b. As a part of this, please carefully compute and label: i. All asymptotes (e.g. low-frequency & high frequency) ii. All corner frequencies ii. The frequency and magnitude (in dB) of any resonances (if they exist) 50 x 10-3H 000 0.252 Vin(t) 0.2F 11 Vout(t) Figure 2: System for Question 3

the worst case. 4: Show that there are at most [n/2h+1] nodes of height h in an n-element heap