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Consider the slender tower shown in Figure E4.19, which vibrates in the transverse direction shown in the figure.20 It is made from reinforced concrete. An estimate for the first natural frequency of this system is 0.15 Hz. The logarithmic decrement values measured for the tower with uncracked reinforced concrete material and cracked reinforced concrete material are 0.04 and 0.10, respectively. If a wind gust induces an initial displacement of 0.5 m and an initial velocity of 0.2 m/s, determine the peak displacement amplitudes in the cases with uncracked concrete material and cracked concrete material.
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