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The pinned end of a pinned-free beam is given a harmonic motion of amplitude 𝑦0 perpendicular to the beam. Show that boundary conditions result in the equation: 𝑦0 𝑦𝑙 = sinh 𝛽𝑙 cos 𝛽𝑙 βˆ’ cosh 𝛽𝑙 sin𝛽𝑙 sinh 𝛽𝑙 βˆ’ sin𝛽𝑙 Which for 𝑦0 β†’ 0, reduces to: tanh 𝛽𝑙 = tan 𝛽

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Harmonic Motion - Beam
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