The speed of a pendulum bob moving in simple harmonic motion is given by v = 1.26sin(2πt) where v is in m/s and t is time in seconds.
s = ∫ v dt
The Attempt at a Solution
v = 1.26sin(2πt)
Integrating v yields
s = -0.2cos(2πt) + c
and solving for c where s, t = 0 yields c = 0.2 (as cos 2πt = 1 when t = 0), meaning that s = 0.2 - 0.2cos(2πt)
The answer in the back of the textbook seems to ignore this fact, simply stating that the displacement is equal to -0.2cos(2πt).
My question is this: does the constant of integration always matter when integrating like this to find displacements and velocities? Can it be "ignored"? Is the back of my textbook lying to me about the answer?