Question

Differential Equation problem

We know that a force of 2.8 Newtons is required to stretch a certain spring 0.7 meters beyond its natural length. A 1.44-kg mass is attached to this spring and allowed to come to equilibrium. The mass-spring system is then set in motion by applying a push in the upward direction that gives the mass an initial velocity of 1.04 meters per second. Let y(t) represent the displacement of the mass above the equilibrium position t seconds after applying the push. Write an IVP that models this situation and solve it: y(t) Preview syntax error How far away from the equilibrium position will the mass be after 6 seconds? (Round your answer to the nearest 0.01 meters.) meters Now consider another spring. For this second spring we know that a force of 2.8 Newtons is required to stretch it 0.7 meters beyond its natural length, but we also know it has a damping constant of 2 kg/sec. We attach a 1.44-kg mass to this second spring and allow it to come to equilibrium. The new mass-spring system is then set in motion by applying a push in the upward direction that gives the mass an initial velocity of 1.04 meters per second Let z(t) represent the displacement of the mass above the equilibrium position t seconds after applying the push. Write an IVP that models this situation and solve it: z(t) = How far away from the equilibrium position will the second mass be after 0.1 seconds? (Round your answer to the nearest 0.01 meters.) meters

Answer 1

ven -2.8 + k 1-4千 l-44 2. 1-44 y(6)--0.339 2 c-2 2( 44)

0-644t y (t)二 0.694 e ό.cqpt 20. 238 0.694t (0.2%) ,n (4.363t) 0,b69 4 o.176) Sin (o. 4363,) 드o.to3e