1. The problem statement, all variables and given/known data The displacement of a machine is given by the simple harmonic motion as x(t) = 5cos(30t)+4sin(30t). Find the amplitude of motion, and the amplitude of the velocity. 2. Relevant equations x''(t) = -4500cos(30t)-3600sin(30t) 3. The attempt at a solution I should note that I'm not having any difficulty with the problem conceptually, as it is very simple. However, for some reason unknown to me, I'm getting the wrong sign on a t-value when I set x''(t) to zero. I've checked and rechecked my work numerous times, and I'm not sure what's going on. This exact same procedure worked with the first derivative, so I don't get why it's failing me with the second. I've graphed x''(t) on Desmos, and the first positive t-value for x''(t)=0 is 0.0749. My answer is equal to 0.02986. Strangely, according to the graph, the first negative t-value to satisfy x''(t)=0 is -0.02986. Does anyone know why I'm getting the wrong sign? It's driving me absolutely insane. Please see the attached photo to view my attempt at a solution. It is admittedly quite late here, and while there must be some pernicious error in my algebra, I can't find it. Thank you!