- #1
Saracen Rue
- 150
- 10
Homework Statement
A cantilever of length ##L## is rigidly fixed at one end and is horizontal in the unstrainted position. If a load is added at the free end of the beam, the downward deflection, ##y##, at a distance, ##x##, along the beam satisfies the differential equation: [tex]\frac{d^2y}{dx^2}=k\left(L-x\right) \ for\ 0\le x\le L[/tex]
Where ##k## is a constant. Find the deflection, ##y##, in terms of ##x## and hence find the maximum deflection of the beam.
Homework Equations
Basic knowledge of integration
The Attempt at a Solution
After double integrating both sides I'm left with ##y=\frac{k}{2}Lx^2-\frac{k}{6}x^3+cx+d## As the question tells us the beam is horizontal when their is no weight on it, we know that ##y=0## when ##x=0##.
##0=\frac{k}{2}L\left(0\right)^2-\frac{k}{6}\left(0\right)^3+c\left(0\right)+d##
##d=0##
##y=\frac{k}{2}Lx^2-\frac{k}{6}x^3+cx##
This is where I get stuck - I can't find any part of the question which helps me calculate the value of the constant ##c##. The answer says that ##c## should be zero, but I don't understand how they know this.