Building Science
Solved internal forces exercises: shear and bending moment diagrams
Six exercises with solutions: simply supported beam with a uniform load and with two point loads, off-centre load, cantilever with combined loads,…
Archive
Month: November 2026
6 articles
Building Science
Internal forces in depth: beam element, area rule, cantilever and point load
The equilibrium of the beam element, the area rule for drawing shear and moment by hand, the cantilever with a tip load…
Telecom Electronics
Solved oscillator exercises: Colpitts, Clapp, phase noise and crystal
Six exercises with solutions: frequency and start-up of a Colpitts, the Clapp variant, phase noise with Leeson's model, reciprocal mixing in a…
Telecom Electronics
Oscillators in depth: designing a Colpitts, the crystal and Leeson's phase noise
Step-by-step design of a Colpitts oscillator, the Clapp variant, the electrical model of the crystal with the series and parallel resonances proved,…
Systems Theory
Solved reachability and controllability exercises, from basic to exam level
Six exercises with solutions: Kalman's test, systems with two inputs, reachability with a parameter, companion form, minimum energy of the double integrator,…
Systems Theory
Reachability in depth: the Gramian computed, the minimum-energy input and the PBH test
The Gramian of the double integrator computed step by step, the input that moves the state and the proof that it is…