A bird of mass \(2 \mathrm{~kg}\) sits at the end of a horizontal branch of a tree as shown in Fig. 2.92. The branch has a length of \(4 \mathrm{~m}\) from the trunk of the tree with a diameter of \(0.1 \mathrm{~m}\). If the density of the branch is \(700 \mathrm{~kg} / \mathrm{m}^{3}\) and the Young's modulus is \(10 \mathrm{GPa}\), determine the following:

a. Equation of motion of the bird considering the weights of the bird and a uniformly distributed weight of the branch.

b. Natural frequency of vibration of the branch with the bird.

Transcribed Image Text:

Fo Crown of tree Mc Top of trunk Bottom of trunk (a) FIGURE 2.91 Trunk of a tree subjected to force. (b)