Trebuchet Dynamics

$1.$ select a trebuchet design and determine the equations that govern a trebuchet using the supplied reading, resources on the internet, and$/$or any other resources you can find.

$2.$ Draw a FBD of a simple two$-$dimensional version of a trebuchet of your choice.

$3.$ Choose three design variables that you will vary related to the trebuchet design or projectile, and assign values to all other unknown variables. Justify your choices for assigning values to chosen known variables.

$4.$ Use the computational tool of your choice $($Matlab$,$ C$++,$ Excel, or other$)$ to implement the equations with your three chosen variables which you will vary. Assign at least $10$ values across a range of one of your three chosen design variables. You may set your other two chosen variables to a constant value while you assess the third variable.$$

$5.$ Calculate the launch distance of the projectile as a function of each of your three chosen design variables individually. Evaluate how the range of your chosen variables influence launch distance.

$6.$ Bonus: optimize each of your three variables simultaneously to find the longest launch distance based on all three chosen variables.

$7.$ Write a one$-$page written description which includes your FBD$,$ equations, assumptions with justification, assigned variables with justified values, and three chosen variables. Write the equations to describe the distance that the trebuchet will launch an object. Describe the assumptions that you must make to use those equations. This can be hand$-$written in our HW format.