Q)1 A pendulum has a maximum displacement of A = 2.5m and a frequency f = 6 Hz. The displacement at any time x in general form can be represented by the following equation:
x= A sin(ωt)
where A = Maximum displacement, ω= Angular velocity= 2πf, t= Time
(i) Find the two times when the displacement is 90 cm
(ii) The linear velocity of oscillation is given by the following equation:
v = ωAcos(ωt)
Determine the time t for the oscillation to reach a velocity of -19m/s
Q) 2. Using the Power Series expansion:
(i) verify the voltage across the capacitor in Task 3 after a time of 5 seconds.
(n.b. expand the function to include 10 terms)
3. Reduce the following Algebraic functions into partial fractions.
a. 7x + 25/(x+4)(x+3)
b. 24 + 23x + 5x2/(2x + 3)(x + 2)2
c. 27x2 - 4x + 5/(2x + x + 6x2) (x-3)
4 Show how to simplify the following using quotient and remainder methods :
a. 5x2 + 7x -2/(x +2)
b. 16x3 - 19x2 -3x + 2 /(2x -3)