Question

Координата тела, выраженная в сантиметра изменяется с течением времени следуещим оброзом: x=3.5cos4пи t. чему равны амплитуда колебаний и циклическая частота? Чему равна фаза колебаний спустя 5 секунд после начала калебаний?

Answer 1

А=3,5 см     (0,035 м)
ω=4*π=12,56 рад/с
φ=4*π*t=4*π*5=20*π
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Answer 2

To find the amplitude and cyclic frequency of the body's oscillations, as well as the phase of the oscillations after 5 seconds, we can analyze the given equation: x = 3.5cos(4πt).

Amplitude of Oscillations:

The amplitude of oscillations can be determined by looking at the coefficient in front of the cosine function. In this case, the coefficient is 3.5. Therefore, the amplitude of the oscillations is 3.5 centimeters.

Cyclic Frequency:

The cyclic frequency, also known as angular frequency, can be determined by looking at the coefficient of 't' inside the cosine function. In this case, the coefficient is 4π. Therefore, the cyclic frequency is 4π radians per unit of time.

Phase of Oscillations after 5 seconds:

To find the phase of the oscillations after 5 seconds, we need to substitute the value of 't' into the equation x = 3.5cos(4πt) and solve for 'x'.

Substituting t = 5 into the equation: x = 3.5cos(4π * 5) x = 3.5cos(20π)

To find the value of cos(20π), we can use the fact that cos(2π) = 1. Since 20π is equivalent to 10 periods of the cosine function, cos(20π) will also be equal to 1.

Therefore, the phase of the oscillations after 5 seconds is 1 centimeter.

Please note that the given equation assumes the body starts at its equilibrium position at t = 0.