Please try and answer all of them, at least briefly. :) Thank you! LAB 2.1 Two M
ID: 1998368 • Letter: P
Question
Please try and answer all of them, at least briefly. :) Thank you! LAB 2.1 Two Magnets and a Spring In this lab we consider the motion of a mass that can slide freely along the w-axis. The mass is attached to a spring that has its other end attached to the point (0,2) on the axis. In addition, the made of iron and is attracted to two magnets of equal strength-one located at the point (-1. -a) and the other at 1. -a) (see Figure 2.67). We assume that the spring obeys Hooke's Law. and the magnets attract the mass with a force proportional to the inverse of the square of the distance of the mass to the magnet (the inverse square law). If we choose the spring constant, mass. strength of the magnets, and units of distance and time appropriately, then we can model the motion of the mass along the r-axis with the equation 0.3x A good exercise for engineering and physics student s: Derive this equation and de- termine the units and choices of spring constant. rest length of the spring, mass, and strength of the magnets involved.) The goal of this lab is to study this syst ly. Use technology to find equilibria and study the behavior of solutions. Be careful to consider the correct regions of the phase plane at the correct scale so that you can find the important aspects of the In your report, you should address the following items: 1. Consider the system with the parameter value a 2.0. Discuss the behavior of solutions in the phase plane. Relate the phase portrait to the possible motions of the mass along the x-axis. Figure 2.67 Schematic of a mass sliding on the r-axis attached to a spring and a racted hy two magnets. 229
Explanation / Answer
1) Please follow this link for the plot :
https://www.wolframalpha.com/input/?i=plot+(-0.3x)+-+((x-1)%2F((x-1)%5E2+%2B+4)%5E(1.5))+-+((x%2B1)%2F((x%2B1)%5E2+%2B+4)%5E(1.5))
2) Please follow this link for the plot :
https://www.wolframalpha.com/input/?i=plot+(-0.3x)+-+((x-1)%2F((x-1)%5E2+%2B+0.25)%5E(1.5))+-+((x%2B1)%2F((x%2B1)%5E2+%2B+0.25)%5E(1.5))
4) for a=2.0
https://www.wolframalpha.com/input/?i=plot+(-0.3x)+-+((x-2)%2F((x-2)%5E2+%2B+4)%5E(1.5))+-+((x%2B2)%2F((x%2B2)%5E2+%2B+4)%5E(1.5))
for a=0.5
https://www.wolframalpha.com/input/?i=plot+(-0.3x)+-+((x-2)%2F((x-2)%5E2+%2B+0.25)%5E(1.5))+-+((x%2B2)%2F((x%2B2)%5E2+%2B+0.25)%5E(1.5))