Question

Материальная точка совершает гармонические колебания по закону х=2sin ( 1/4 пt+1/2п) где х- в см t=в.с определить амплитуду колебаний А начальную фазу Ф период колебаний T. C дано, формулами и решением

Answer 1

Уравнение гармонических колебаний
x(t)=Asin(ωt+α)
А - это амплитуда. В нашем случае она равна 2см
ω - угловая скорость. Она равна π/4
α - начальная фаза. Равна π/2

Период колебаний ищем по формуле
T=2π/ω=8 секунд

Answer 2

Harmonic Oscillations of a Material Point

The equation given describes the harmonic oscillations of a material point. Let's break down the equation and determine the amplitude, initial phase, and period of the oscillations.

The equation is given as:

x = 2sin(1/4πt + 1/2π)

Where: - x represents the displacement of the material point in centimeters (cm). - t represents time in seconds (s).

To find the amplitude (A), we can observe that the coefficient of the sine function is 2. Therefore, the amplitude of the oscillations is A = 2 cm.

To determine the initial phase (Φ), we can compare the given equation to the standard form of a harmonic oscillation equation:

x = A sin(ωt + Φ)

Comparing the two equations, we can see that the initial phase is given by Φ = 1/2π.

Finally, to find the period (T) of the oscillations, we need to determine the angular frequency (ω). The angular frequency is given by the coefficient of t in the equation. In this case, the angular frequency is 1/4π. The period is the reciprocal of the angular frequency, so we have:

T = 2π/ω = 2π/(1/4π) = 8 seconds (s).

Therefore, the period of the oscillations is T = 8 s.

In summary: - Amplitude (A) = 2 cm - Initial phase (Φ) = 1/2π - Period (T) = 8 s

Please let me know if there's anything else I can help you with!