The point oscillates harmoniously with an amplitude of 3 cm, a frequency of 20 Hz, an initial phase of п / 6

| May 18, 2021 | education

The point oscillates harmoniously with an amplitude of 3 cm, a frequency of 20 Hz, an initial phase of п / 6. Find the equation of this oscillation, the speed and acceleration of the point for any moment of time.

v = 20 Hz.

φ0 = п / 6.

x (t) -?

V (t) -?

a (t) -?

The equation of harmonic oscillations has the form: х (t) = А * sin (φ0 + ω * t), where А is the amplitude of oscillations, φ0 is the initial phase, ω is the cyclic frequency.

ω = 2 * P * v.

x (t) = 3 * sin (P / 6 + 40 * t).

The dependence of the speed is a derivative of the coordinate: V (t) = x (t) “.

The dependence of the acceleration is the derivative of the speed: a (t) = V (t) “.

V (t) = x (t) “= (3 * sin (п / 6 + 40 * t))” = 3 * cos (п / 6 + 40 * t) * (п / 6 + 40 * t) ” = 3 * cos (п / 6 + 40 * t) * 40 = 120 * cos (п / 6 + 40 * t).

a (t) = V (t) “= (120 * cos (п / 6 + 40 * t))” = – 120 * sin (п / 6 + 40 * t) * (п / 6 + 40 * t) “= – 120 * sin (п / 6 + 40 * t) * 40 * t = – 4800 * sin (п / 6 + 40 * t).



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