Q$-3.$ A beam is loaded as shown with variables as listed below:

P: $1500lb$

M: $1200lb.ft$

E: $29000$ksi

L: $9ft$

M

Cross section of beam is a rectangle with:

Height: $10$ in

Width $($base$)$: $2$ in

a$.$ Use the double integration method to find a function for vertical deflection and then find the deflection at $x=\frac{L}{4}.$

b$.$ Verify your answer using the method of superposition