CLASS TEST $1($MODULE I$)$ TIME: $1H$ FULL MARKS: $10$

Figure $1$ shows an arrangement of reciprocating agitator. The flywheel rotates to drive the disc agitator to do up$-$down reciprocation within the cylinder of tank diameter $($T$)0\mathrm{.}286m$ for fluid mixing. The diameter of the agitator disc $($D$)$ is $0\mathrm{.}204m$ and its thickness $(t)$ is $0\mathrm{.}003m.$ The reciprocation displacement is given by $z(t)=A[1-cos(2ft)+(\frac{A}{2}L)(1-cos(4ft))],$ where amplitude $(A)=0\mathrm{.}04m,$ frequency $(f)=1\mathrm{.}75Hz,L=0\mathrm{.}25m$ and $H=0\mathrm{.}4m.$ Due to some instrumental issue the flywheel comes to a steady state after some time of its start, which impacts the instantaneous speed of the reciprocation. Calculate the time required for the flywheel to come to a steady state. Use Newton$-$Raphson method with two iterations only.

$[(CO2)($ Analysis $\frac{?}{\text{H}\text{O}\text{C}\text{Q}})]$

$5+5=10$

FIGURE $1$