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A cantilever of length $l$, and flexural rigidity $EI$, stiffened by a spring of stiffness $k$, is loaded by a transverse force $P$, as shown.

The transverse deflection under the load is

  1. $\dfrac{Pl^3}{3EI} \begin{bmatrix} \dfrac{3EI}{3EI+2kl^3} \end{bmatrix}$
  2. $\dfrac{Pl^3}{3EI} \begin{bmatrix} \dfrac{6EI-kl^3}{6EI} \end{bmatrix}$
  3. $\dfrac{Pl^3}{3EI} \begin{bmatrix} \dfrac{3EI-kl^3}{3EI} \end{bmatrix}$
  4. $\dfrac{Pl^3}{3EI} \begin{bmatrix} \dfrac{3EI}{3EI+kl^3} \end{bmatrix}$
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