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(Solved): (1) Motor, Pulley & Spring: Rotation of top pulley \theta _(1)(t) Rotation of bottom pulley \the ...
(1) Motor, Pulley & Spring:
Rotation of top pulley \theta _(1)(t)
Rotation of bottom pulley \theta _(2)(t)
Translation of bottom pulley x(t)
Motor torque applied to top shaft \tau
Top shaft has moment of inertia I with pulley radius r_(1)
Bottom moving pulley has mass m and radius r_(2)
Spring k is at rest length when motion variables are zero
Cable wraps around both pulleys and does not slip
Give the equation of motion of the complete system N_()
TERMS OF x(t) :