Two masses m1 and m2 are connected to two springs A and B of negligible mass,...

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Two masses m1 and m2 are connected to two springs A and B of negligible mass, having stiffened of kland k2 respectively. The two springs are attached as shown in the figure. Let x1 t and x2 t respectively the vertical displacement of m1 and m2 from their equilibrium position, assuming no external forces is impressed on the system and no damping force is presented. The motion of the coupled system is represented by the following two simultaneous 2nd order O.D.E's *1 = -6x1+4 (x2-x1)x2 = -4 x2 - x1 With I.C's: x1(0)= x2(0 )= 0 x1(0) = 1 x2(0) = -1 (1) Use Hein's method to evaluate x1(10) &x2(10) with At = 0.1 sec and 3- corrections for each step. (ii) Use the results in part (1) to evaluate x1(20) &x2(20) with At = 0.1 sec using the 4th order Raung- Kutta Method. Two masses m1 and m2 are connected to two springs A and B of negligible mass, having stiffened of kland k2 respectively. The two springs are attached as shown in the figure. Let x1 t and x2 t respectively the vertical displacement of m1 and m2 from their equilibrium position, assuming no external forces is impressed on the system and no damping force is presented. The motion of the coupled system is represented by the following two simultaneous 2nd order O.D.E's *1 = -6x1+4 (x2-x1)x2 = -4 x2 - x1 With I.C's: x1(0)= x2(0 )= 0 x1(0) = 1 x2(0) = -1 (1) Use Hein's method to evaluate x1(10) &x2(10) with At = 0.1 sec and 3- corrections for each step. (ii) Use the results in part (1) to evaluate x1(20) &x2(20) with At = 0.1 sec using the 4th order Raung- Kutta Method.

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To use Heins method we need to first rewrite the secondorder ODEs as a system of firstorder ODEs Let v1 and v2 be the velocities of m1 and m2 respectively Then we have x1 v1 v1 6x1 6x2 x2 v2 v2 4x2 x1 ... View the full answer