Jerk is the rate of change. (i.e. the derivative with respect to time of the acc

Question

Jerk is the rate of change. (i.e. the derivative with respect to time of the acceleration) If riding in a car, the ride is "jerky" it is because the change in acceleration is abrupt. Suppose the position function of a piston in a cylinder has the equation: s(t)=Acos(2(pi)bt) where A and b are both constants. b is the frequency of the pistons motion, i.e. how many times per second the piston moves up and down. (pi=3.14159...) Part A: Find an expression for the jerk of the piston with s(t)=Acos(2(pi)bt) Part B: Suppose we double the frequency of the piston.. it is moving up and down twice as often per second. The position function is now s(t)=Acos(2(pi)bt) What effect does this have on the jerk? (Is it twice as big? Half as big?)

Explanation / Answer

A) velocity, v = ds/dt

= A*(-sin(2*pi*b*t))*(2*pi*b)

= -2*A*pi*b*sin(2*pi*b*t)

acceleration, a = dv/dt

= -2*A*pi*b*cos(2*pi*b*t)*(2*pi*b)

= -A*(2*pi*b)^2*cos(2*pi*b*t)

jerk, J = da/dt

= -A*(2*pi*b)^2*(-sin(2*pi*b*t))*(2*pi*b)

= A*(2*pi*b)^3*sin(2*pi*b*t))

B) when b becomes 2 times, The jerk becomes 8 times

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