Question

Ускорение маятника, совершающего гармонические колебания, зависит от времени согласно уравнению a=2cos4,5t, где все величины выражены в СИ. Найти циклическую частоту колебаний и амплитуду колебаний ускорения

Answer 1

Ускорение маятника, совершающего гармонические колебания, зависит от времени согласно уравнению a=2cos4,5t, где все величины выражены в СИ. Найти циклическую частоту колебаний и амплитуду колебаний ускорения

Дано а= 2*cos 4,5*t
  w - ? амах-?
Из уравнения видно что w=4,5 с^-1 - циклическая частота
аmax=2 м/с2 - амплитуда ускорения

Answer 2

To find the cyclic frequency and amplitude of the acceleration of a pendulum undergoing harmonic oscillations, we can use the given equation: a = 2cos(4.5t), where all quantities are expressed in SI units.

Cyclic Frequency (Angular Frequency):

The cyclic frequency, also known as the angular frequency, is denoted by the symbol ω (omega) and represents the number of complete oscillations per unit time. It is related to the period of oscillation (T) by the equation ω = 2π/T.

In this case, we need to find the period of oscillation. The period is the time taken for one complete oscillation. To find the period, we can use the fact that the cosine function completes one full cycle (from 0 to 2π) when its argument (4.5t) increases by 2π.

Setting 4.5t = 2π, we can solve for t to find the period: 4.5t = 2π t = (2π) / 4.5

Now we can calculate the period (T) and then find the cyclic frequency (ω): T = (2π) / 4.5 ω = 2π / T

Let's calculate the cyclic frequency:

T = (2π) / 4.5
ω = 2π / T

Amplitude of Acceleration:

The amplitude of acceleration represents the maximum value of acceleration during the oscillations. In this case, the amplitude is given as 2 in the equation a = 2cos(4.5t).

Let's summarize the findings:

- Cyclic Frequency (Angular Frequency): ω = 2π / T - Amplitude of Acceleration: 2

Please note that the values of the cyclic frequency and amplitude of acceleration will depend on the specific values of time (t) during the oscillations.