Chapter 11.1, Problem 11.13P

A Scotch yoke is a mechanism that transforms the circular motion of a crank into the reciprocating motion of a shaft (or vice versa). It has been used in a number of different internal combustion engines and in control valves. In the Scotch yoke shown, the acceleration of point A is defined by the relation a $a=-1.8\sin kt$ , where a and t are expressed in m/s² and seconds, respectively, and $k=3$ rad/s. Knowing that $x=0$ and $v=0.6$ m/s when $t=0$ , determine the velocity and position of point A when $t=0.5$ s.