The mathematical pendulum for the time interval t1 = 20c, made the same number of complete oscillations

The mathematical pendulum for the time interval t1 = 20c, made the same number of complete oscillations as the spring pendulum for the time interval t = 10c. How many times do the oscillation frequencies of pendulums differ?

The oscillation period is such a period of time during which the body returns to the same point from which it began its movement.
T = t / n, where n is the number of oscillations, t is the time during which the body made these oscillations.
T = t / n
The oscillation period depends on the frequency according to the law:
T = 1 / ν
Let us express the frequency from this expression:
ν = 1 / T = n / t
Let us express n from this expression:
n = ν * t
n1 = ν1 * t1
n = ν * t
Let’s equate n:
ν1 * t1 = ν * t
ν / ν1 = t1 / t
Let’s substitute the data and calculate:
ν / ν1 = t1 / t = 20/10 = 2
Answer: the oscillation frequency of the spring pendulum is 2 times greater.



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