Problem 4.30

Find the period of small oscillations of a mathematical pendulum of length $l$ if its point of suspension $O$ moves relative to the Earth's surface in an arbitrary direction with a constant acceleration $\mathbf{w}$ (Fig. 4.7). Calculate that period if $l=21 \mathrm{~cm}, w=g / 2,$ and the angle between the vectors $w$ and $g$ equals $\beta=120^{\circ}$ .

\begin{aligned} & \text { 4.30. } T=2 \pi V \overline{l /|\mathrm{g}-\mathbf{w}|}=0.8 \mathrm{~s}, \quad \text { where } &|\mathrm{g}-\mathbf{w}|=\\ =& \sqrt{g^{2}+w^{2}-2 g w \cos \beta} \end{aligned}

Mechanical Oscillations