Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Vibrations and Waves · Problem 2-1
The free vibrations of physical systems — A.P. French
Physics — Waves · complex-exponential-representation
Problem Express the following in the form z = R e [ A e i ( ω t + α ) ] z = \mathrm{Re}[Ae^{i(\omega t + \alpha)}] z = Re [ A e i ( ω t + α ) ] z = sin ω t + cos ω t z = \sin \omega t + \cos \omega t z = sin ω t + cos ω t z = cos ( ω t − π / 3 ) − cos ω t z = \cos(\omega t - \pi/3) - \cos \omega t z = cos ( ω t − π /3 ) − cos ω t z = 2 sin ω t + 3 cos ω t z = 2 \sin \omega t + 3 \cos \omega t z = 2 sin ω t + 3 cos ω t z = sin ω t − 2 cos ( ω t − π / 4 ) + cos ω t z = \sin \omega t - 2\cos(\omega t - \pi/4) + \cos \omega t z = sin ω t − 2 cos ( ω t − π /4 ) + cos ω t Browse the problem library