A simple harmonic oscillator SHO consists of a mass M sittin

A simple harmonic oscillator (SHO) consists of a mass, M, sitting on a norizontal frictionless surface and attached to a spFind theg of constant k whose mass can be ignored. The mass is set into motion. The clock is started when the mass is at x = A and is moving toward the negative times direction. Write the equation of motion of this SHO. (b) Now consider a hemispherical bowl of radius R sitting on a horizontal surface. A bead of mass m is released from the rim and is allowed to slide from one side of the bowl to the other in circular motion. The bowl is frictionless except for a small region of lenathe delta

Solution

Equation of motion   

                          Y = A sinwt = A sin (squareroot(K/M))*t

where A is the amplitude

          k = spring constant

         M = mass

         t = time

number of trips

N sintheta = mrw^2

N = mrw^2/sintheta