Answer:
Step-by-step explanation:
A) First .... it is a sine wave with no 'shift' :
sin x
it has a period of 4 ... usually a sine wave has a period of 2 pi
so this wave is 'compressed'.
2 pi / c = 4
c = compression factor = 2 pi / 4 = pi / 2
so now you have
sin ( pi/2 * x )
the amplitude is 4
so the position wave is 4 sin (pi/2 * x)
B) velocity wave is the derivative of the position wave:
= 2 pi cos ( pi/2 * x)
the acceleration wave is the derivative of the velocity wave:
= - pi^2 sin ( pi/2 * x)
C) the gherk wave is the derivative of the acceleration wave :
= - 1/2 pi^3 cos (pi/2 * x)
Here are the velocity and acceleration graphs....you may want to separate them: