Scissor lifts require linear motion to provide elevation. In this project, this mechanism is actuated with the linear motion of a motor at the base providing a displacement x $.$ For this project:

Assume that $x^{}$ is zero, $x^{}$ is a constant that you choose and initial condition for $x$ is $0.$ Plot the height h of the platform as well as $h^{},h^{},,{}^{},{}^{}$ as a function of time.

Assume that $x^{}$ is a constant that you choose and the initial conditions for $x$ and $x^{}$ are $0.$ Plot the height h of the platform as well as $h^{},h^{},,{}^{},{}^{}$ as a function of time.

For the above cases obtain the relationships between input terms $x,x^{},x^{}$ and output terms $h,h^{},,,{}^{},{}^{}$ analytically as closed form equations. Then write a program using Matlab, Python, Excel etc. to plot these values as a function of time. Explain the simulation result with references to your mathematical findings.

For kinematic analysis, masses, inertias and forces acting on the system should be neglected.

Use case $1$ or case $2.$