Aspring hangs vertically; its upper end is fixed and from the lower end a box weighing 19.6 n hangs. once in equilibrium, the box is pulled down by moving it 50 cm and released. knowing that k8 n/m and that the air resistance is negligible, find: (a) the law of movement of the box (b) the time necessary for the box to move from the initial position to 0.25 m above the position of balance. (c) how is the movement afocused if we repeat the experiment with a box that weighs a quarter of the original box? (d) can we change the spring in the original experiment to obtain a movement equivalent to that observed in item (c)? 2. to a spring, which stretches 50 cm when a force of 6 n is applied, a weight of 29.4 n is hung. assuming that the spring and the mass are in a fluid that offers a resistance to movement to study the movement in the following cases: (a) if the weight moves away from its equilibrium position by pulling it down 1 m, then it is released. (b) if weight is lifted, 5 m from its equilibrium position, and then dropped 3. to a spring with a constant of elasticity k 25 n/m, a 5 kg ball is hung. all the spring-mass system is in a fluid that makes the system critically damped. determine: (a) the resistance to movement offered by bluido. (b) the law of movement of the ball, if it is known that at a certain moment it passed through the equilibrium position down with a speed of 10 m/sec. 4. to a spring, which has a constant of elasticity & -5 n/m, a 1 ke pellet is hung assuming that the spring and the mass are in a fluid that offers a resistance to movement of 0.25 to study the movement if it is known that at a certain moment it passed 1.5 m below the equilibrium position with a speed of -1.5 m/sec. 5. interpret and solve the initial value problem 5x"+0.25 +2.5 15sen (2x),x(0) -1, (0) = . 1. or