For the fixed values I = 1, and g = 9.81, give a graphical comparison of your model values of P along with the (theoretically) exact values for 0 c [0, 7]. Note . MATLAB's built-in function for K is ellipke.m, with one adjustment: K (x) = ellipke(z?). Solution . For (a), in the absence of air resistance , the period of a pendulum should depend on the length of the pendulum , I, the force of gravity, 9, and the angle the pendulum is pulled from the vertical, 0. We look for dimensionless products 1 = 10gbgepd, with dimensions 1 = L' L 'T -2end This gives the dimension equations L : 0 =a+c T : 0 = - 2c+ d. For m, we choose while for #2 we choose d = 1 to get c= _ and a = - , giving IT 2 According to Buckingham's Theorem we can express the equation for the period of a pen - dulum in the form f ( 1 , 1 2) = 0, and the Implicit Function Theorem suggests there exists some function o(", ) so that 72 = $ (7 1 ). I.e., PV " = $(0 ), and so P = $(0)V -. We solve (b) with the M-file pdatafit.m