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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 304

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

[2]
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3 Unit A2 1: Pure Mathematics (A-level only) Questions

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