The displacement of a structure is defined by the following equation for a damped oscillation:

y = 9 e –kt cost wt

Where k = 0.7 and ω = 4.

(a) Use the graphical method to make an initial estimate of the timer required for the displacement to decrease to 3.5.

(b) Use the Newton-Raphson method to determine the root to εs = 0.01%

(c) Use the secant method to determine the root of εx = 0.01%.