problem1) The 20-lb collar slides along smooth rod. If the collar is released from rest at A, find out its speed with it passes point B. The spring has an unstretched length of 3 ft.
problem2) A centrifugal pump with smooth radial vanes rotates in horizontal plane with constant angular velocity, w. Determine the magnitude of force exerted by a vane on a particle of mass m as it moves out along the vane. The particle is introduced at r = r_{0} with no angular velocity. Suppose there is no shear (i.e., friction) force between the particle and vane.
problem3) Find out the area under the following function for 0
a) use simpson's rule
b) use the quad function
y=x^3 * cos(x)