Question

(3) (20 points) The (dimensionless) equations of motion for a frictionless double pendulum system as shown below (in the figure on the left) with mi m2 and L1 L are The solutions are graphed below (on the right) for the initial conditions θι (0) 2, θ1(0) 1.02(0) 0, and 02(0)-0 for oS t s 50. (a) Reformulate the IVP as a first order system.2 (b) Generate approximate solutions using any method (Euler, improved Euler, Runge-Kutta, NDSolvo, ode45) and graph θί and θ2 as functions of t. Your graph should look like the one below (right). 81 L. 4π 02 01 40 50

please use mathematica for code NOT MATLAB

Answer 1

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, Activities Mathematica Sat 15:09 MdtneifidLIcd difi-to-vseteilchlittree阿蚱sadddy student Edition-Personal Use Only File Edit Insert Format Cel Graphics Evaluation Pale WOLFRAM MATHEMATICA STUDENT EDITION Demonstrations MathWorldIWolfram Communty IHelp mi-)- s-NDSolve【(x ' ' [t] + (y'' [t] * Cos(x[t]-y[t]]) + (y' [t] ^2 * Sin(x(t]-y[t]]) + sin(x[t] ] , x → InterpolatingFunction Domain: fftO.. 2.81)) Output: scalar y InterpolatingFunction Domain:((0., 2.81) Output:scalar 04A: n- Plot [Evaluate(xIt]) /. s], (t, «, 50)] 20 40 50 5.0x 1062 -1.0 1083 -1.5x1063 2.0x 1063 unyo -2.5 10 Plot [Evaluate [{y[t)) ,. s), s], (t, 0, 50)] (t, o, se)) . 10 20 40 50 -2 x 1006 uny -7 x 1006 100%

Activities Mathematica 崋 Sat 15:0s diff.nb- Wolfram Mathematica 11.3 Student Edition - Personal Use Only File Edit Insert Format Cell Graphics Evaluation Palettes Window Help WOLFRAM MATHEMATICA STUDENT EDITION ParametricPlot [Evaluate [ {x[t], y[t]} /. s], {t, o, 50)] Demonstrations MathWorldIWolfram Communty IHelp m( 11056 2M 1063x10564x1056510561067x105 2 x 10 -3 x 106 -4 x 1056 5 1056 6 x 106 -7 1056 100%