A mass, m, is hung from an ideal spring (its length is equal to zero and no friction) and reaches equilibrium at position B when the spring has been stretched to the length l. The mass is then pulled to position C and released. The position C is of height h below the position B. The mass oscillates between positions A and C. [Neglect friction.] At which position, A, B, or C, is mass m located when the kinetic energy, gravitational potential energy, or elastic potential energy of the system is at a maximum? Explain the reason for each case.

5. The pendulum shown below consists of a 30 kg point mass at the end of a uniform bar with mass m = 45 kg and length L = 2 m. The pendulum moves in a vertical plane while acted upon by a 500 N-m torque as shown. If the pendulum's angular velocity is 4 rad/s when 0 = 90 degrees, how much force is exerted on the pendulum by the pin at point A when 0 = 330 degrees? 500 N-m B F = 2470 N Z -52 degrees

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Question 2: A point-mass M of mass m is tied to a string which winds around a cylinder like a bobbin. The string is pinned on the cylinder at some point, and P denotes the point at which the string leaves the bobbin and starting from which it is taut. The cylinder has radius a and rotates at a constant rate around the vertical axis of the fixed frame F (which is also the axis of symmetry of the bobbin). The motion takes place in the hori- zontal plane, which is assumed frictionless. See figure. (a) Find a relationship between l, a and expressing that the length of the string is constant (b) Compute the velocity and acceleration of point M with respect to F. (c) Apply LMB in F to the system consisting of the point mass M alone (don't forget to start with a free body diagram!). Deduce a differential equation for l as well as the value of the string's tension in terms of the other parameters. (d) (bonus) Solve the differential equation for l. eo Ω Mas P M FIGURE 1 - The spinning bobbin.…