A double pendulum, defined by the parameters $m_1,m_2$ and $l,$ is$,$ additionally, held by a rotational spring with stiffness $c,$ as shown in the figure below. The rotational spring is relaxed at the position ${}_1=0.$

Remark: ${?}_{(}()c)os({}_1)cos({}_2)+sin({}_1)sin({}_2)=cos({}_1-{}_2)$

Given: $,m_1=0,63kg,m_2=0,37kg,l=0,2m,g=9,81m{s}^{-2},c=118kg{s}^{-2},$

Insert the correct solution at an accurracy of four significant numbers into the corresponding fields:

a$)$ Evaluate the potential energy of the system with respect to the given terms. $(\frac{2}{2}\frac{?}{2}$ points$)$

$=,cos({}_1)+,cos({}_2)+,si{n}^2({}_1)$

$kg{m}^2{s}^{-2}$

b$)$ Evaluate the kinetic energy of the system with respect to the given terms. $(\frac{2}{2}\frac{?}{2}$ points$)$

$T=,{}_1^{}{?}^2+,{}_2^{}{?}^2+,{}_1^{}{}_2^{}cos({}_1-{}_2)$

$[kg{m}^2{s}^{-2}]$