Homework $1$

Problem $3$:

For the three systems shown below, x $1$ and x $2$ are the equilibrium positions when $f=0.$

Therefore, all three systems $($a$),($b$)$ and $($c$)$ will have the same equations of motion and response. Draw the

free body diagrams and derive the equations of motion by Newton's method and Euler$-$Lagrange. Note: With

x $1$ and $x2=0$ as static equilibrium, your equation of motion will be exactly the same for all the three systems

i$.$e$.($a$),($b$)$ and $($c$)$ and the mg will not appear in the equation of motion.

$($a$)$

$($b$)$

$($c$)$