The speed of the object is the 1st derivative of its displacement.
The acceleration is the 2nd derivative of the displacement. That's also the first derivative of speed. Either way you approach it, we have to take the displacement and differentiate twice.
Displacement = x(t) = 20 cos(5t) meters
Speed = x'(t) = -100 sin(5t) m/s
Acceleration = x''(t) = -500 cos(5t) m/s²
At time t=0.5π sec,
Acceleration = -500 cos(2.5π) m/s²
cos (2.5π) = cos(0.5π) = zero
This is weird. At t=0.5π sec, the acceleration of the oscillating mass appears to be zero.
My math must be kerflooie, but I'm too tired right now to stay and pick at it. I'll just resign myself to having my answer reported, and I hope whoever reports it will be kind enough to point out the error of my ways.
