Question

Вычислить частоту,период и циклическую частоту колебаний тела,совершающегося 150 колебаний за мин.

Answer 1

Частота ∨-это число колебаний тела за единицу времени=n/t
то есть v=150/60=2,5Гц
Период-это обратная величина, т.е. Т=1/v=1/2,5=0,4 сек
Циклич частота w=2п/T=2п/0,4=15,7 рад/сек

Answer 2

Calculation of Frequency, Period, and Angular Frequency

To calculate the frequency, period, and angular frequency of an object that completes 150 oscillations per minute, we can use the following formulas:

Frequency (f): The number of oscillations per unit of time. Period (T): The time taken to complete one oscillation. Angular Frequency (ω): The rate of change of angular displacement with respect to time.

The relationship between these three quantities is given by the following equations:

f = 1 / T ω = 2πf

Let's calculate the frequency, period, and angular frequency using the given information.

1. Frequency (f): The object completes 150 oscillations per minute. To find the frequency, we divide the number of oscillations by the time taken.

f = 150 oscillations / 1 minute

2. Period (T): The period is the reciprocal of the frequency. To find the period, we divide 1 by the frequency.

T = 1 / f

3. Angular Frequency (ω): The angular frequency is calculated by multiplying the frequency by 2π.

ω = 2πf

Now, let's calculate the values.

1. Frequency (f): Using the given information, we have:

f = 150 oscillations / 1 minute

Therefore, the frequency is 150 oscillations per minute.

2. Period (T): To find the period, we divide 1 by the frequency:

T = 1 / f

Substituting the value of f:

T = 1 / 150 oscillations per minute

Therefore, the period is 1/150 minutes per oscillation.

3. Angular Frequency (ω): The angular frequency is calculated by multiplying the frequency by 2π:

ω = 2πf

Substituting the value of f:

ω = 2π * 150 oscillations per minute

Therefore, the angular frequency is 300π radians per minute.

To summarize: - The frequency of the oscillations is 150 oscillations per minute. - The period of the oscillations is 1/150 minutes per oscillation. - The angular frequency of the oscillations is 300π radians per minute.

Please note that the above calculations are based on the given information and the formulas for frequency, period, and angular frequency.