Answer Happy

4. [20 pts] The following figure depicts the tape drive of a mainframe computer. Tape is handled by an idler wheel and a take-up capstan. K and B represent the spring constant and the damping of tape stretch, respectively, J₁, J₂ are the mass moments of inertia, B₁, B₂ are the viscous damping constants for the take-up capstan and the idler wheel, K, is the motor torque constant, w₁ and we are angular velocities. Constant force F is applied to the tape by means of a vacuum column. A positive current applied to the DC motor will provide a torque on the capstan in the clockwise direction as shown by the arrow. Assume that positive angular velocities of the two wheels are in the directions shown by the arrows. a) Obtain the equations of motion (for tape and wheels) in terms of the parameters given. Find the value of current that just cancels the force, F and then eliminate the constant current and its balancing force, F from your equations. x₂ No friction K J₁, B₁ (Cia= u de motor Take-up capstan Head Idler wheel J₂, B₂ Vacuum column