Question

I need to rescale (4) from the first page to the equation on the second page.

2.[60pts.] A bead of mass m is constrained to slide along a straight rigid horizontal wire. A spring with natural length Lo and spring constant k is attached to the bead and to a support point a distance h from the wire. See Figure 1. Let z(t) denote the position of the bead on the wire at time t. (Note that x is measured from the point on the wire directly above where the spring attaches to its support. So z 0 exactly when the spring is vertical.) Wire Figure 1: Bead on horizontal wire. Assume four forces act on the bead. Gravity with acceleration g exerts a constant force straight down on the bead. The spring exerts a force on the bead of the form -k(length of spring - Lo)u, bead. The motion of the bead along the wire is opposed by a frictional force bi: parallel to the wire. Finally, the wire exerts a reaction force on the bead. This force acts perpendicular to the wire. Applying Newton's Second Law, we see that satisfies the equation where x = dr/dt and x = d2x/dt2. (You do ** NOT ** need to show (4).) (a)[6pts.] Find a rescaling to rewrite (4) as where ε-mk/b2 and I = Lo/h are dimensionless groupings

Answer 1

d t To 2. tI- て

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