a double pendulum as shown in Fig. $1$ is requested to be implemented in Simulink Simscape

Fig. $1.$ A double pendulum made of springs, dampers and mass blocks

The left part of Fig. $1$ shows the structure of the double pendulum, while the right part gives

the parameters. m $1$ and m $2$ are the mass of the two blocks. k$1,$ k $2$ are the coefficients of the

two springs. g$1,$ g$2$ are the damping factor of the springs. That means the springs are not

ideal, but they will exhaust energy when they are compressed or dragged.

$1\mathrm{.}1$ Using the Simscape toolbox in Simulink, build the system, and visualize the movement

using Multibody objects.

$1\mathrm{.}2$ Given initial values of x$1$ and x$2,$ observe the behavior of the system, and display their

time domain response.

$1\mathrm{.}3$ Derive the mathematical model of the system and simulate the obtained model in

Simulink.

$1\mathrm{.}4$ Compare the time domain responses of the model and the physical system you built in

Simscape.

$1\mathrm{.}5$ Comment on the transient responses using the key indicators.