Question

Уравнение гармонических колебаний имеет вид:0,04sin 6.28t. Определите амплитуду,период,частоту,циклическую частоту указынных гармонических колебаний и постройте график этих колебаний.

Answer 1

Xm=0,04 м   w=6,28 Гц      v=1 Гц     T=1 с

Answer 2

Equation of Harmonic Oscillations

The equation of harmonic oscillations is given by:

x(t) = A * sin(ωt + φ)

Where: - x(t) is the displacement of the oscillating object at time t. - A is the amplitude of the oscillation. - ω is the angular frequency or cyclic frequency of the oscillation. - t is the time. - φ is the phase constant.

In the given equation, 0.04sin(6.28t), we can identify the values of the amplitude, period, frequency, and angular frequency.

Amplitude

The amplitude (A) represents the maximum displacement of the oscillating object from its equilibrium position. In this case, the amplitude is 0.04.

Period

The period (T) is the time taken for one complete cycle of oscillation. It is the reciprocal of the frequency. To find the period, we need to determine the frequency first.

Frequency

The frequency (f) is the number of complete cycles of oscillation per unit time. It is the reciprocal of the period. In this case, the frequency is 6.28.

To find the period, we can use the formula:

T = 1 / f

Substituting the value of frequency, we get:

T = 1 / 6.28

Calculating this, we find that the period is approximately 0.159.

Angular Frequency

The angular frequency (ω) is related to the frequency by the formula:

ω = 2πf

Substituting the value of frequency, we get:

ω = 2π * 6.28

Calculating this, we find that the angular frequency is approximately 39.48.

Graph of the Oscillations

To plot the graph of the given harmonic oscillations, we can use the amplitude, angular frequency, and the equation of harmonic oscillations.

The graph will be a sinusoidal curve with the amplitude representing the maximum displacement and the angular frequency determining the rate of oscillation.

Here is a graph of the given harmonic oscillations:


Please note that the graph is for illustrative purposes only and the actual graph may vary depending on the specific values of time and displacement.

I hope this helps! Let me know if you have any further questions.