Question

Маятник совершил 50 колебаний за 1 минуту 40 секун. найти период частоту и циклическую частоту колебаний

Answer 1

1минута 40 секунд = 100 секунд
100секунд : 50колебаний = 2колебаний /секунду

Answer 2

1 колебание за 2 секунды.

Answer 3

Calculation of Period, Frequency, and Angular Frequency

To find the period, frequency, and angular frequency of the oscillations of the pendulum, we need to use the given information that the pendulum completed 50 oscillations in 1 minute and 40 seconds.

Let's start by calculating the period of the pendulum. The period is the time taken for one complete oscillation. We can calculate it by dividing the total time by the number of oscillations:

Period (T) = Total time / Number of oscillations

Given that the total time is 1 minute and 40 seconds, we need to convert it to seconds:

1 minute = 60 seconds

So, the total time in seconds is:

1 minute + 40 seconds = 60 seconds + 40 seconds = 100 seconds

Now, we can calculate the period:

T = 100 seconds / 50 oscillations

T = 2 seconds

The period of the pendulum is 2 seconds.

Next, let's calculate the frequency of the pendulum. The frequency is the number of oscillations per unit time. It is the reciprocal of the period:

Frequency (f) = 1 / Period (T)

Substituting the value of the period we calculated earlier:

f = 1 / 2 seconds

f = 0.5 Hz

The frequency of the pendulum is 0.5 Hz.

Finally, let's calculate the angular frequency of the pendulum. The angular frequency is the rate at which the pendulum rotates in radians per unit time. It is calculated by multiplying the frequency by 2π:

Angular Frequency (ω) = 2π * Frequency (f)

Substituting the value of the frequency we calculated earlier:

ω = 2π * 0.5 Hz

ω ≈ 3.14 radians/second

The angular frequency of the pendulum is approximately 3.14 radians/second.

To summarize: - The period of the pendulum is 2 seconds. - The frequency of the pendulum is 0.5 Hz. - The angular frequency of the pendulum is approximately 3.14 radians/second.

Please let me know if there's anything else I can help you with!