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Mechanical Oscillations

Problem 4.33

Find the time dependence of the angle of deviation of a mathematical pendulum 80 cm80 \mathrm{~cm} in length if at the initial moment the pendulum (a) was deviated through the angle 3.0∘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 m/s0.22 \mathrm{~m} / \mathrm{s} (c) was deviated through the angle 3.0∘3.0^{\circ} and its lower end was imparted the velocity 0.22 m/s0.22 \mathrm{~m} / \mathrm{s} directed toward the equilibrium position.

Reveal Answer
 4.33. (a) θ=3.0∘cos⁡3.5t ;  \text { 4.33. (a) } \theta=3.0^{\circ} \cos 3.5 t \text { ; } (b) θ=4.5∘sin⁡3.5t\theta=4.5^{\circ} \sin 3.5 t (c) θ=\theta= =5.4∘cos⁡(3.5t+1.0)=5.4^{\circ} \cos (3.5 t+1.0). Here is expressed in seconds.
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