1. The problem statement, all variables and given/known data A .25 kg block oscillates on the end of a spring with a force constant of 200 N/m. If the oscillation started by elongating the spring 0.15 m and giving the block a speed of 3 m/s, (a) what is the amplitude of the oscillation, and (b) If the clock is started when the block is at the right hand extreme of its motion, how long does it take to reach a point where the kinetic energy of the block equals the elastic potential energy stored in the spring? 2. Relevant equations x(t) = Acos (ωt + phase angle) v(t) = -ωAsin(ωt + phase angle). 3. The attempt at a solution I know that the first part of this question can be solved using energy relationships, but I tried to use the x = Acos (ωt + phase angle) and v(t) = -ωAsin(ωt + phase angle). I divided v(t) by x(t) and got 3/0.15 = -[(rad)(k/m)][tan(phase angle)] 20 = -28.28tan(phase angle) phase angle = -.616 radians I then went back to the the x(t) equation and plugged this value in: .15 = Acos[28.28(0) - .616] A = 0.18 m My first question is, is this method valid? The correct answer is 0.18, but just making sure this reasoning is sound. If so, I don't understand why I can't carry this information into part (b) of the question. My reasoning for the 2nd part was that 1/2kx^2 = 1/2kA^2 Therefore, x = 0.13. I then plugged this into the x(t) equation from above: .13 = .184cos(28.28t - .616) This gave a t of .0496 seconds. However, my professor did not include a phase angle of -.616 in his answer; his phase angle is 0. What am I doing wrong?!?!