The Acceleration vs Time graph would actually be a sinusoidal curve, not a straight line. Perhaps you were thinking of acceleration vs displacement. If so; start with the general displacement-time equation for a simple pendulum, use it to find an acceleration-time equation, and compare the two.
No its not sinusoidal , see the attached image , the third graph is Acceleration vs Time of Simple Pendulum ...why these are straight lines ?
and also see the second graph , why Velocity vs time is not sinusoidal but in Mass attached to spring it is Sinusoidal
What is there I am meant to explain. I'm telling you it's not correct. How much thought have you even put into this? Do you understand that velocity and acceleration are the first and second time derivatives of displacement respectively. Do the graphs you drew reflect that?