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436 chapter 16Figure 16.7 A simulation of a projectile shot into a group of particles. (Courtesy of J. Wetzel.)16.5 Quiz1. We wish to make an MD simulation by hand of the positions of particles 1and 2 that are in a 1-D box of side 8. For an origin located at the center of thebox, the particles are initially at rest and at locations x i (0) = −x 2 (0)=1. Theparticles are subject to the force⎧10, for |x 1 − x 2 |≤1,⎪⎨F (x)= −1, for 1 ≤|x 1 − x 2 |≤3,⎪⎩0, otherwise.(16.23)Use a simple algorithm to determine the positions of the particles up until thetime they leave the box. Make sure to apply periodic boundary conditions.Hint: Since the configuration is symmetric, you know the location of particle 2by symmetry and do not need to solve for it. We suggest the Verlet algorithm(no velocities) with a forward-difference algorithm to initialize it. To speedthings along, use a time step of h =1/ √ 2.−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 436