We consider a Euler-Bernoulli beam, clamped at one extremity and free at the other, to which are attached a piezoelectric actuator and a collocated sensor touching the clamped extremity. We provide an output feedback law and characterize the sensor/actuator lengths for which the strong stabilization holds. Finally, we prove that the energy decreases to zero in a polynomial way for almost all lengths, and in an exponential way for lengths admitting a certain coprime factorization.