A double pendulum, defined by the parameters $m_1,m_2$ and $l,$

is$,$ additionally, held by a spring with stiffness $c,$ as shown in the

figure below. The springs remains always horizontal and is relaxed

at ${}_1=0.$

Remark: $cos({}_1)cos({}_2)+sin({}_1)sin({}_2)=cos({}_1-{}_2)$

Given:

$m_1=0,58kg,m_2=0,46kg,l=0,1m$

$g=9,81m{s}^{-2},c=421kg{s}^{-2}$

Insert the correct solution at an accurracy of four significant num$-$

bers into the corresponding fields:

a$)$ Evaluate the potential energy of the system with respect to the

given terms. $(\frac{2}{2}\frac{?}{2}$ points$)$

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

b$)$ Evaluate the kinetic energy of the system with respect to the

given terms. $(\frac{2}{2}\frac{?}{2}$ points$)$

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

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