# Dynamic Trading: Dynamic Concepts in Time, Price & Pattern by Robert Miner

By Robert Miner

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Additional resources for Dynamic Trading: Dynamic Concepts in Time, Price & Pattern Analysis With Practical Strategies for Traders & Investors

Example text

Thus: I(c)K ' 500 A - (s + 200)(s + 800) , s + 200 B s + 800' Multiplying the fractions by (s + 200)(s + 800), we find that: 500 = A(s + 800) + B(s + 200) =» A = 5/6, B = -5/6. We find that the solution of the equation is: i(t) = | ( e - 2 0 O t - e - 8 0 0 t ) « ( * ) where the current is measured in amperes. A Look at Resonance^—An Example Consider the equation satisfied by a spring-mass system with an m Kg mass and a spring whose spring constant is k N/M that is being excited by a sinusoidal force of amplitude A newtons and angular frequency Q, rad/sec.

If the function does not have a limit, then the theorem does not apply, and when the theorem does not apply one can get nonsensical results if one uses the theorem. The Delayed Unit Step Function—An Example Consider the function f(t) = u(t — a),a > 0. Clearly, here afinalvalue does exist; thefinalvalue of a delayed unit step function is 1. The Laplace transform of the delayed 13 Mathematical Preliminaries unit step function is (according to Theorem 7): From the final value theorem, we see that: lim u(t - a) = lim sC{u(t - a))(s) s—*0+ t—>oo e~as = lim s 8-»0+ S = lim e~as = 1.

Here are a number of examples of legal assignments. 30 A Mathematical Introduction to Control Theory (1) A = 3. This assigns the value 3 to the variable A. It also causes MATLAB to print: A = 3 (2) Generally, if one wishes to suppress printing one ends the assignment with a semi-colon. The command A = 3; also assigns three to the variable A, but it does not cause anything to be printed. (3) MATLAB prints the value of a variable if one types the variable's name. If one types A, MATLAB responds with: A = 3 (4) B = [3, 4 , 5 ] ; assigns the array [3, 4, 5] to B.