Question

3. A 20 cm long horizontal spring (k= 200 N/m) is attached to a wall. A 2 kg box is attached to the other end. You pull the box 3 cm, displacing the spring from equilibrium. Assume the floor is frictionless. a. If the box is released from rest at t = 0 s: i. Write an equation describing the position of the box at some arbitrary time "t". Go ahead and fill in the values for amplitude, phase angle, and angular frequency. ii. How close does it get to the wall? iii. At what time does it get to this position? b. You do this a second time but instead of releasing it from rest, you give it a push of 1 m/s toward the wall at t = 0 s. Take the equation you found in part A and adjust the amplitude and phase angle to match this new motion. 2 mis

Answer 1

cü x = A Cos (wt) p=00 A = 3cm 200 SA 2 Sine x=to 3 Cos Clout) In lige form 3 Sin (lott To ) se - o = 1 for sin egh. ☺) Close to 17 cm wall = 20- 3 Ciii at ta Ha 2 T= (2) 10 2T z 0.314 sec lox2 (6) 1 KA2 = {kx² + + mv² 8 (200) C003) + 2.00 2 2 Az o.1044 m 200 * 10.44 cm 3 10.44 10.44 Caset +0 ) = Cas cord) = 1.2.79 rad Ao Sin (wtto) d. 10.44 Cos (10 t +1.279)