Question By using the Laplace table (y(t) Y(s) in the Appendix A.1, compute the Laplace transforms for the following time-domain function: a) f(t) = t sin 3t - 2t cost b) f(t) = 5.5e-* + 3 e 2 + 2.5 t e-3t

d. A pipe is connected to the large reservoir that supplied liquid to the pipe. If the head loss at the pipe entrance is V2 given as K then the value of K is: 2g'

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

Receivables amount to P150,000. Receivable turnover is \( 10 \mathrm{x} \) and inventory is maintained at a level equal to 15 days' sales. Selling price per unit is P100 and has gross profit ratio of \( 40 \% \). A proposal has been made to change the term credit to \( \mathrm{n} / 60 \) to result to an increase in sales volume by one-third or by 5,000 units. Under this proposal, bad debts losses are estimated at \( 1 \% \) to \( 3 \% \) of sales but inventory turnover shall remain the same. How much is the increased accounts receivable? How much is the increased inventory? Compute for the increased operating income.