Show that the shape (r( varphi) ) for a central spring force ellipse takes the standard form (r 2 a 2 b 2 left(b 2 cos 2 varphi a 2 sin 2 varphi ight) ) if (in equation 7 37) we use the plus sign in the denominator and choose ( varphi 0 pi 4 ) Data from equation 7 37 7(6) Im EVE kl m) sin 2(0 0)...

Show that the shape (r(varphi)) for a central spring force ellipse takes the standard form (r^{2}=a^{2} b^{2}

Question:

Show that the shape $r(\varphi)$ for a central spring force ellipse takes the standard form $r^{2}=a^{2} b^{2} /\left(b^{2} \cos ^{2} \varphi+a^{2} \sin ^{2} \varphi\right)$ if (in equation 7.37) we use the plus sign in the denominator and choose $\varphi_{0}=\pi / 4$.

Data from equation 7.37