Question

A 500-g block is attached to the free end of a spring that has a 5.0-N/m stiffness, while the other end is fixed. It is pulled 15 cm and released. We start recording at t=0, when it is 8.0 cm to the left of the equilibrium position and moving to the left. (a) What is the phase constant? (b) What is the position, velocity and acceleration of the block immediately after a 2.0-s interval has elapsed? (13 points)

Answer 1

'; w= K - 5 500 X10-3 = Jio n W: 3.16 A = 15 cm = 0.15 m *=-8cm =-0.08m (a) :: 8 = Sint 1) = sint (-0:08) = 82 II -5.72 rad (b)x= A Sin wt +) X = 0.15 Sin (3.16* 2 +5.72) X -0.15 Sin (12:04) -0.07 m re

w = Aw Can (wtto) v = (0.15)(3.16) (an (3.16 X2 +5.72) = 0.474 Con 12:04 V-0.41 m/s 2 a = - Aw' Sin (wt +) a : - (0.15) (10) Sin 12.04 a: 0.75 m 10?