For the system shown below, the free vibration response is given in terms of the motion of the rack as follows:

$x=6cos3\mathrm{.}2t$

where $x$ is expressed in cm and $t$ in seconds. Determine the followings:

a$)$ The peak angular displacements of gears A and $B$ in degrees.

b$)$ The maximum angular velocities and accelerations of gears A and $B.$

c$)$ The angular displacement, velocity and acceleration of gear $A$ at $t=1\mathrm{.}3s.$

Ans. ${}_{A_{\text{m}\text{a}\text{x}}}=0\mathrm{.}429$rad,${}_{A_{\text{m}\text{a}\text{x}}}^{}=1\mathrm{.}37ra\frac{d}{s},{}_{A_{\text{m}\text{a}\text{x}}}^{}=4\mathrm{.}39ra\frac{d}{s^2}$

$($:${}_A(1\mathrm{.}3)=-0\mathrm{.}225$rad,${}_A^{}(1\mathrm{.}3)=1\mathrm{.}169ra\frac{d}{s}({}^{}).\mathrm{.}12$