Question

(35pt) A kid is swinging on a swing (gravity is pointing down, see figure). The swing has a friction which is proportional to the velocity. Specifically: |Ffric| =(m/4)*sqrt(gl)*θ' . (3) (a) (5pt) Write down the equation of motion of the θ direction of the polar coordinates. (b) (30pt) Assume small oscillations and that the kid has the following initial conditions θ(t = 0) = θA and ˙θ(t = 0) = 0. (i) (10pt) Find the frequency of the oscillations as a function of g and l. (ii) (20pt) Find θ(t) as a function of θA, g, and l.

Skip no steps, please be as detailed as possible.

Answer 1

As the value of frictional force is qiven, i found that is sqrt(g/l) is it is sqrt(g*l) then accordingly calculation will change....

Rest of the process will same.