A particle of mass m is attachedbetween two identical springs on a horizontal frictionless table.Both springs have spring constant k and are initially un-stretched.If the particle is pulled a distance x along a directionperpendicular to the initial configuration of the springs, theforce exerted by the springs on the particle is given by F =-2kx(1-(L/sqrt(x^2+L^2)))
a) determine the amount of work done by this force in moving theparticle from x = A to x = 0.
b) show that the potential energy of the system is U(x) = kx^2 +2kL(L - sqrt(x^2 + L^2))
c) make a plot of U(x) versus x and identify all equilibriumpoints.
d) assume that m = 1.81 kg, L = 1.20 m and k = 40.0 N/m. If theparticle is pulled 0.500 m to the right and then released, what isits speed when it reaches the equilibrium point x = 0?
