Question

Изменения силы тока в зависимости от времени задана уравнением I=20cos100ПТ. Определите частоту и период колебаний и амплитуду силы тока.

Answer 1

Амплитуда силы тока Im=20A
циклическая частота ω=100 π   1/c
частота =ω/2π=100π/2π=50 Гц
период Т=1/ν=1/50=0,02 с

Answer 2

Determining the Frequency, Period, and Amplitude of the Current

The equation given to describe the current as a function of time is I = 20cos(100πt). Let's break down the components of this equation to determine the frequency, period, and amplitude of the current.

Amplitude of the Current

The amplitude of the current can be identified directly from the given equation. In this case, the amplitude is 20.

Frequency and Period of the Current

To find the frequency and period, we can use the standard form of a cosine function: y = A cos(Bx - C) + D. In this form: - A represents the amplitude - B is the coefficient of x which determines the frequency - The period can be calculated using the formula: Period = 2π / |B|

Calculating the Frequency

From the given equation I = 20cos(100πt), we can compare it to the standard form to find the frequency: - A = 20 (amplitude) - B = 100π (coefficient of t)

By comparing with the standard form, we can determine that the frequency is 100 Hz.

Calculating the Period

Using the formula Period = 2π / |B|, we can calculate the period: - |B| = 100π - Period = 2π / 100π = 1 / 50 seconds

Therefore, the period of the current is 1/50 seconds.

In summary, the frequency of the current is 100 Hz, the period is 1/50 seconds, and the amplitude is 20.