# Please show work Two particles of m_1 and m_2 are connected by a light, inextensible string...

###### Question:

Two particles of m_1 and m_2 are connected by a light, inextensible string of total of mass length L, which passes through a smooth hole in a smooth horizontal table. The mass m_2 is suspended below the table, and the mass m_1 moves in a circular motion on the table with an initial distance R_0 from the hole. A gravitational field g acts on this system. The mass m_1 starts out with speed v_0 on the table initially at right angles to the string. (a) Find, but do not solve, the equations of motion for m_1 and moves only m_2, if m_2 moves only in a vertical line. (b) Assume initial conditions were such that equilibrium nearly held and solve for the equilibrium distance R_e, when R = 0. Solve the equations of motion for small departures from equilibrium. Describe this motion.

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