1. The problem statement, all variables and given/known data A particle with a mass of 0.5 kg is attached to a horizontal spring with a force constant of 50 N/m. At the moment t = 0, the particle has a maximum speed of 20 m/s and is moving to the left. (a) Determine the particle's equation of motion. (b) Where in the motion is the potential energy three times the kinetic energy? (c) Find the minimum time interval required for the particle to move from x=0 to x=1.00m. (d) Find the length of a simple pendulum with the same period. 2. Relevant equations (a) w=sqrt(k/m) v_max = Aw (b) 3(.5*m*w^2*A^2*sin^2(wt+phi))= .5*k*A^2*cos^2(wt+phi) 3. The attempt at a solution I searched he forums here for the same question and found this thread: https://www.physicsforums.com/archive/index.php/t-231270.html I think I understand how to find omega and the maximum velocity (though the signs may be incorrect), but I don't understand how to solve for phi. The only thing I could think of was to set v=-wAsin(wt+phi) to -20=10*(-2)sin(phi) for t=0. This returned a phi=3pi/2 or -pi/2, unless I'm doing something wrong. I also tried to set x(0)=0, so 0=(-2)cos(phi) which results in phi=pi/2. These answers disagree with what the linked thread found for phi and what my professor's answer had for phi. I'm just having a hard time understand phi, which seems like such a simple concept. If anyone could steer me in the right direction, I think I could finish this problem. Thanks for any help!