In a Laplace Transform Table, the Laplace transfer function of f(t) is F(s). When d(t) = f(t) then 1 = F(s). When x(t) = f(t) then X(s) = F(s). If d(t) is the impulse of a spring when d(t) = kx(t), then derive the equation for the impulse of a spring as X(s) in term of k. Next question : A controller has a transfer function a and the other controller has a transfer function b. The overall transfer function of both controllers is ab. What is the transfer function overall when both controllers have similar transfer function 1 / (Cs k)?
Answer / kang chuen tat (malaysia - pen
For f(t), d(t) = kx(t). Transform such equation to F(t) gives 1 = kX(s) then X(s) = 1 / k. Next answer : Overall transfer function for 2 controllers in combination is 1 / (Cs k) x 1 / (Cs k) = 1 / [ (Cs k) (Cs k) ]. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS 61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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Question 53 - In the purchase of a machine with a period n = 8.5 years, the minimum attractive rate of return, i = 12 %, the cost P = $55000, F = $4000 is the salvage, annual maintenance A = $3500. The return of the investment or equivalent uniform annual benefit is $15000. The equivalent uniform annual cost is P (A / P, i, n) + A - F (A / F, i, n). The investment is considered acceptable only when equivalent uniform annual benefit is greater than the equivalent uniform annual cost. From the compound interest table, (A / P, i = 12 %, n = 8 years) = 0.2013, (A / P, i = 12 %, n = 9 years) = 0.1877, (A / F, i = 12 %, n = 8 years) = 0.0813, (A / F, i = 12 %, n = 9 years) = 0.0677. Prove by calculations whether the investment above is acceptable.
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