$($a$)$ Let $a,b>0$ and let a point of mass $m$ move along the curve in $R^3$ defined by $c(t)=(acost,$bsint,$t^2).$ Describe the curve and find the tangent line at $t=.$

$($b$)$ Find the force acting on the particle at $t=.$

$($c$)$ Define the function $E(z)$ by

$E(z)={\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}\sqrt[\phantom{2}]{1-z^{2}si{n}^{2}t}dt$

Find a formula for the circumference of the ellipse

$\frac{x^2}{a^2}\frac{y^2}{b^2}=1$

where $E(z)0,in$ terms $ofE(z).$