A mass of 3 kg stretches a spring 12 cm. The mass is acted on by an external force of 10 sin (½) N (newtons) and moves in a medium that imparts a viscous force of 3 N when the speed of the mass is 3 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 9 cm/s, formulate the initial value problem describing the motion of the mass. (Use g = 9.8 m/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds. Use up for u' and upp for u".) , u(0) = 0 m, u'(0) = m/s Hint: The damping coefficient y is determined from the statement that yu' = Fvisc = 3 N when the speed of the mass is u' = 0.03 m/s. Now compute gamma.

A mass of 3 kg stretches a spring 12 cm. The mass is acted on by an external force of 10 sin (½) N (newtons) and moves in a medium that imparts a viscous force of 3 N when the speed of the mass is 3 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 9 cm/s, formulate the initial value problem describing the motion of the mass. (Use g = 9.8 m/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds. Use up for u' and upp for u".) , u(0) = 0 m, u'(0) = m/s Hint: The damping coefficient y is determined from the statement that yu' = Fvisc = 3 N when the speed of the mass is u' = 0.03 m/s. Now compute gamma.