Question

Коливання точки відбувається за законом х = А соs(ωt+φ).В деякий момент часу зміщення точки дорівнює 5 см, її швидкість 20 см/c і прискорення -80 см/с 2 . Знайти амплітуду, циклічну частоту, період коливань і фазу в даний момент часу.

Answer 1

Ответ:

Ответ:

A = 7,07 см; ω = 4 рад/с; T = 1,57 с; (ωt+φ) = –π/4 рад

Answer 2

Given Information:

- Equation of motion: x = A cos(ωt + φ) - Displacement of the point at a certain moment: x = 5 cm - Velocity of the point: v = 20 cm/s - Acceleration of the point: a = -80 cm/s^2

Finding the Amplitude:

The amplitude (A) of the oscillation is the maximum displacement from the equilibrium position. In this case, the displacement of the point at a certain moment is given as 5 cm. Therefore, the amplitude is A = 5 cm.

Finding the Angular Frequency:

The angular frequency (ω) is related to the period (T) of the oscillation by the equation ω = 2π/T. Since the period is the time taken for one complete cycle of oscillation, we can find it by dividing the time taken for the point to complete one cycle by the number of cycles. However, we don't have the time taken for one cycle or the number of cycles given in the information provided. Therefore, we cannot directly calculate the angular frequency.

Finding the Period:

The period (T) of the oscillation is the time taken for one complete cycle. It is related to the angular frequency (ω) by the equation T = 2π/ω. Since we don't have the angular frequency, we cannot directly calculate the period.

Finding the Phase:

The phase (φ) in the equation of motion represents the initial phase of the oscillation. It determines the position of the point at t = 0. Unfortunately, we don't have the value of the phase given in the information provided. Therefore, we cannot calculate the phase.

Summary of Findings:

- Amplitude (A): 5 cm - Angular Frequency (ω): Not enough information provided to calculate. - Period (T): Not enough information provided to calculate. - Phase (φ): Not enough information provided to calculate.

Please note that without the values of the angular frequency, period, and phase, we cannot fully determine the characteristics of the oscillation.