Write the equation of oscillations of a thread pendulum if the amplitude of oscillations is 20 cm

Write the equation of oscillations of a thread pendulum if the amplitude of oscillations is 20 cm, and the period is 2 s., The initial phase is 0.

The equation of harmonic vibrations of a thread pendulum is as follows:

x = A * sin (Ɵ0 + ωt), where A is the amplitude of oscillations of the pendulum (by the condition A = 20 cm = 0.2 m), Ɵ0 is the initial phase of oscillations (by the condition Ɵ0 = 0), ω is the cyclic frequency (you can determined by the equation of motion), t is the oscillation time of the thread pendulum.

We express the cyclic frequency in terms of the period known by the condition (T = 2 s):

ω = 2Π / T.

x = 0.2 * sin (0 + (2Π / 2) t) = 0.2 * sin Πt.

Answer: The equation of oscillations is x = 0.2 * sin Πt.