All Problems Mechanical Oscillations
Problem 4.33
Find the time dependence of the angle of deviation of a mathematical pendulum \(80 \mathrm{~cm}\) in length if at the initial moment the pendulum (a) was deviated through the angle \(3.0^{\circ}\) and then set free without push; (b) was in the equilibrium position and its lower end was imparted the horizontal velocity \(0.22 \mathrm{~m} / \mathrm{s}\) (c) was deviated through the angle \(3.0^{\circ}\) and its lower end was imparted the velocity \(0.22 \mathrm{~m} / \mathrm{s}\) directed toward the equilibrium position.
\[ \text { 4.33. (a) } \theta=3.0^{\circ} \cos 3.5 t \text { ; } \] (b) \(\theta=4.5^{\circ} \sin 3.5 t\) (c) \(\theta=\) \(=5.4^{\circ} \cos (3.5 t+1.0)\). Here is expressed in seconds.