Question

Маятник зробив 50 коливань за 1хв 40 с. Визначити період, частоту і циклічну частоту коливань

Answer 1

T=t N=2 c. -период

v=1 T=0,5 Гц. -частота

w=2*pi*v=pi Гц. - циклическая частота

Answer 2

Calculation of Period, Frequency, and Angular Frequency

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

Period is the time taken for one complete oscillation. It can be calculated using the formula:

Period (T) = Total time / Number of oscillations

In this case, the total time is 1 minute and 40 seconds, which is equivalent to 100 seconds. The number of oscillations is given as 50.

Period (T) = 100 seconds / 50 oscillations = 2 seconds

Therefore, the period of the pendulum is 2 seconds.

Frequency is the number of oscillations per unit time. It can be calculated using the formula:

Frequency (f) = 1 / Period (T)

Substituting the value of the period we calculated earlier:

Frequency (f) = 1 / 2 seconds = 0.5 Hz

Therefore, the frequency of the pendulum is 0.5 Hz.

Angular Frequency is the rate of change of angular displacement with respect to time. It can be calculated using the formula:

Angular Frequency (ω) = 2π / Period (T)

Substituting the value of the period we calculated earlier:

Angular Frequency (ω) = 2π / 2 seconds = π radians/second

Therefore, the angular frequency of the pendulum is π 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 π radians/second.

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