Answer
The velocity will be doubled,
the acceleration will be quadrupled,
the jerk will be increased by 8 times,
Work Step by Step
Step 1. Given the motion equation $s(t)=Acos(2\pi bt)$, we have
velocity: $v(t)=s'(t)=-2\pi bAsin(2\pi bt)$
acceleration: $a(t)=v'(t)=-(2\pi b)^2Acos(2\pi bt)$
jerk: $j(t)=a'(t)=(2\pi b)^3Asin(2\pi bt)$
Step 2. When doubling the frequency $b_1=2b$, we have the following results:
velocity: $v(t)=s'(t)=-2\pi (2b) Asin(2\pi (2b) t)=-4\pi bAsin(4\pi bt)=$
acceleration: $a(t)=v'(t)=-(4\pi b)^2Acos(4\pi bt)$
jerk: $j(t)=a'(t)=(4\pi b)^3Asin(4\pi bt)$
Step 3. Examinining the new amplitude gives:
the amplitude of velocity will be doubled,
the amplitude of acceleration will be quadrupled,
the amplitude of jerk will be increased by 8 times,
