a; For the problems below, you will compute the motion of a particle subject to an acceleration a(x) = -4 sin with initial position x(0) = 0 and velocity v(0) = 1. The problems will require you to carefully calculate the derivative of this acceleration as well as its potential energy. 1. Using the modified integration scheme including the analytical jerk term: = acc(x;) jerk(Xi, Vi) 21+1 Li + vidt + } qidt Vi+1 Vi + aidt + } jidt ti+1 = ti + dt (10 points. Write code to calculate the energy error AE(8t) = maxi|Eti) - E(0), where t = idt for a given dt. You may reuse code from class. Be careful when taking the time derivative of the acceleration, as shown in class. (10 points) Compute and print the energy error for each value of St starting with dt = 0.5, and decreasing t by factors of 2 until St