5. Consider a mass m connected to a spring with force constant k. The spring is

ID: 2968346 • Letter: 5

Question

5. Consider a mass m connected to a spring with force constant k. The spring

is connected on the other end to an immovable wall. The mass is initially

displaced from its equilibrium position by a distance of x0. The surface over

which the mass moves is considered to be rough. Therefore a friction force

opposing the motion is present and proportional to the velocity. Take this

constant of proportionality to be

. The mass will be released from rest.

a. Write down the Dynamical System governing this physical situation.

ie. the associated initial value problem

b. Solve this IVP subject to the constraint:

gamma^2 = 4mk

c. Calculate the coordinates: (t, x(t)) at the minimum if

gamma = m = x0 = 1

d. Give a physical interpretation of the minimum point.

This is a HORRIBLE answer and does not help at all. You didnt even solve the questions which were being asked.

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