Question

Сила тока в катушке индуктивности изменяется по закону i=0,001 cos ( 6 пи t + пи/ 4) определите период, частоту колебаний, максимальное значение силы тока и начальную фазу колебаний

Answer 1

Ω=6π=2π/T
T=1/3=0.33 c
v=1/T=3 Гц
Im=0.001 A
φo=π/4   (45°)
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Answer 2

Calculation of Period, Frequency, Maximum Current, and Initial Phase

The given equation for the current in the inductive coil is i = 0.001 cos(6πt + π/4). Let's determine the period, frequency, maximum current, and initial phase of the oscillations.

To find the period, we need to determine the time it takes for the current to complete one full cycle. In this case, the current is a cosine function, and the period can be calculated using the formula T = 2π/ω, where ω is the angular frequency.

The angular frequency can be determined by comparing the given equation to the standard form of a cosine function: i = A cos(ωt + φ). In this case, A = 0.001, ω = 6π, and φ = π/4.

Comparing the equations, we can see that ω = 6π. Therefore, the angular frequency is 6π.

Using the formula for the period, we can calculate:

T = 2π/ω = 2π/(6π) = 1/3 seconds.

The period of the oscillations is 1/3 seconds.

The frequency can be calculated using the formula f = 1/T. Substituting the value of T we just calculated, we find:

f = 1/(1/3) = 3 Hz.

The frequency of the oscillations is 3 Hz.

To find the maximum value of the current, we can use the formula Imax = |A|, where A is the amplitude of the cosine function. In this case, A = 0.001.

Therefore, the maximum value of the current is 0.001 Amps.

Finally, the initial phase of the oscillations can be determined by comparing the given equation to the standard form of a cosine function. In this case, φ = π/4.

Therefore, the initial phase of the oscillations is π/4 radians.

In summary: - The period of the oscillations is 1/3 seconds. - The frequency of the oscillations is 3 Hz. - The maximum value of the current is 0.001 Amps. - The initial phase of the oscillations is π/4 radians.

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