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Finding Magnification factor M for Frequency Ratio

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1) In the idealized model attached shown, m = 15 kg, k = 135 N/m, and the viscous damping ratio is 0.15. Assume that an external harmonic force F(t) = 15 cos 4 t acts on the system with F0=15 N and forcing frequency of 4 rad/s.
i) Find the magnification factor M for the frequency ratio r of 1.382.
ii) What is the amplitude of the response X?

For i ), which one is correct answer:
(a) 4
(b) 3
(c) 1

For ii ), which one is correct answer:
(a) 0.127
(b) 0.184
(c) 0.274

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The solution finds the magnification factor M for frequency ratio. The amplitude of response X is determined.

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