The displacement of an instrument subjected to a random vibration test, at different instants of time, is found to be as follows: Displacement, y, (inch) 0.144 Station, i Time, t (sec) 1 0,05 0.10 0.172 3 0.15 0.213 0.20 0.296 0.25 0.070 6. 0.30 0.35 0.085 7 0.525 8 0.40 0.110 0.45 0.50 0.55 0.60 0.062 10 0.055 11 0.042 12 0.035 a) Please use MATLAB function diff to find the velocity acceleration and jerk based on forward-difference with a step size, At, of 0.05. Please plot t vs. y dy d curve, and t vs. curve, t vs. curve, t vs. curve, respectively. b) Please use MATLAB functions polyfit by fitting a 11th-degree polynomial for the d?y dy and jerk dt3 data and use polyval and diff to find the velocity acceleration dt2 dy curve, t vs. dt d?y drz curve, and t vs. Please plot t vs. y curve, t vs. curve, de respectively. c) Please use MATLAB functions spline by fitting a Not-a-knot Cubic Spline to find the velocity dy acceleration and jerk Please plot t vs. y curve, t vs. curve, t dy curve, and t vs. -curve, respectively. Vs. Please note that the above t vs. y curves should be plotted on one graph (3 curves), t dy dy Vs. curves on one graph (3 curves), t vs. z curves on one graph (3 curves) and t dt VS. curves on one graph (3 curves), respectively. Totally 4 graphs.