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Originally Posted by threewingedfury
well - I didnt use an integral - I was thinking along the lines of a cosine function and how its considered negative and it has a phase constant of 0.
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the way i approached this problem is essentially as follows:
you are given the function for the displacement : x(t) = x_m*cos(wt+p).
you have the initial conditions. x(0)=0, dx/dt=-k, where k is some unknown negative quantity. you can deduce two values of p (not considering periodicity) from the x(0)=0 condition. To determine which value it is, you consider the derivative of the displacement function, dx/dt. the derivative of the displacment function is the velocity. it is positive at one point, and negative at the other. therefore, you need to determine the sign of the derivative of x(t) in order to determine which value is the correct one for your problem.