Find the frequencies of the transverse modes

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Reference no: EM131383537

A uniform rod BC has mass M and length 2a. The end B of the rod is connected to a fixed point A on a smooth horizontal table by an elastic string of strength α¹, and the end C is connected to a second fixed point D on the table by a second elastic string of strength α².

In equilibrium, the rod lies along the line AD with the strings having tension T0 and lengths b, c respectively. Show that the frequency of the longitudinal mode is ((α₁ + α₂)/M)^1/2 and that the frequencies of the transverse modes satisfy the equation

b²c²µ² - 2bc(2ab + 3bc + 2ac)µ + 6abc(2a + b + c) = 0.

where µ = Maω²/T₀. [The calculation of Vapp is very tricky.]

Find the frequencies of the transverse modes for the particular case in which a = 3c and b = 5c.

Reference no: EM131383537

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