The displacement x(t)x(t)x(t) of a physical structure subjected to harmonic wind loading is modelled by the function x(t)=20cos(ωt)+21sin(ωt)x(t) = 20 \cos(\omega t) + 21 \sin(\omega t)x(t)=20cos(ωt)+21sin(ωt).
Given that
20cos(ωt)+21sin(ωt)≡Rcos(ωt−α) 20 \cos(\omega t) + 21 \sin(\omega t) \equiv R \cos(\omega t - \alpha) 20cos(ωt)+21sin(ωt)≡Rcos(ωt−α)find the value of RRR, representing the maximum displacement of the structure, where R>0R > 0R>0.
Circle the correct answer from the options below:
212121 \qquad 292929 \qquad 414141 \qquad 841841841
