A 1.2-kg block rests on a frictionless surface and is attached to a horizontal spring of constant k = 27 N/m. The block is oscillating with amplitude 10 cm and phase constant phi = -pi/2. A block of mass 0.80 kg is moving from the right at 1.7 m/s. It strikes the first block when the latter is at the rightmost point in its oscillation. The collision is completely inelastic, and the two blocks stick together.
a) Determine the frequency of the resulting motion.
I have found this to be 0.58 Hz, and this is the answer.
b) Determine the amplitude of the resulting motion.
E = (1/2)kx^2 + (1/2)mv^2 = 1/2k(A_new)^2 (I think?)
kx^2 + mv^2 = k(A_new)^2
(27)(.1)^2 + (.8)(1.7)^2 = (27)(A_new)^2
A_new = .332
This is what I get, but it does not seem right, and is not accepted as a valid answer... If my approach is wrong, then how do I solve this part?
c) Determine the phase constant (relative to the original t = 0) of the resulting motion.
Well, the relevant equations, I suppose, are:
x = A cos(wt + phi)
v = -w A sin (wt + phi)
a = -w A cos (wt + phi)
However, even once I have the amplitude, I don't know how to solve this part of the question. Please give a hint or something. Thanks.