An applied load at the free end of the beam. The deflection of the beam is the displacement of the free end from its original position. The deflection of a cantilever beam can be calculated using various methods such as the double integration method, the moment-area method, or finite element analysis.

The deflection of a cantilever beam depends on several factors including the length of the beam, the material properties of the beam, the cross-sectional shape of the beam, and the magnitude and distribution of the applied load. In general, a longer beam will have a larger deflection than a shorter beam for the same applied load.

The material properties of the beam, such as its modulus of elasticity and moment of inertia, also affect the deflection. A stiffer material will have a smaller deflection than a more flexible material for the same applied load. The moment of inertia, which is a measure of the beam's resistance to bending, also plays a role in determining the deflection.

The cross-sectional shape of the beam can also influence the deflection. A beam with a larger moment of inertia will have a smaller deflection than a beam with a smaller moment of inertia for the same applied load. This is because a larger moment of inertia provides more resistance to bending.

The magnitude and distribution of the applied load on the beam also affect the deflection. A larger applied load will result in a larger deflection, while a more concentrated load will cause a larger deflection at the point of application.

Overall, the deflection of a cantilever beam is a complex problem that depends on several factors. Calculating the deflection requires knowledge of the beam's geometry, material properties, and the applied load.