text: really confused???? i don't know where to start? a 1.00-kg object is attached to a horizontal spring. the spring is initially stretched by 0.100 m, and the object is released from rest there.  it proceeds to move without friction. the next time the speed of the object is zero is 0.500 s later.  what is the maximum speed of the object okay, this is an example of simple harmonic motion (shm).if the velocity is zero after 0.5s, this means the period of oscillation (t) is 2x0.5s = 1.0sec. if the initial displacement is 0.1m, then the amplitude of oscillation (a) is 2x0.1m = 0.2m. the maximum speed of the object will be achieved when the displacement is 0. the equation for the displacement for shm is:  y = asin(2pift + pi/2) where a is the amplitude, f is the frequency = 1/t and disp = initial displacement, and t = time.  so the velocity is given by the time derivative of displacement:  v = acos(2pift + pi/2) = 0.2cos(2pit + pi/2)  now, since the maximum velocity is achieved after 0.25s (the max velocity is when the object passes through the origin which will be after half the time taken to reach the other end of the cycle);  v = 0.2cos(pi/2 + pi/2) = 0.2cos pi = -0.2m/s  qed