Question

Каков период свободных колебаний нитяного маятника при начальном отклонении от его положения равновесия на 5 см ,если при начальном отклонении от положения равновесия на 20 см период колебаний маятника равен 1 с?

Answer 1

Период колебаний вычисляется по формуле   T = 2*пи* √L/g
период не зависит от амплитуды а зависит от длины значит в том и другом случае
T1=T2 =1c
понятно что при этом L >> A

Answer 2

Period of Free Oscillations of a Pendulum

The period of free oscillations of a pendulum can be calculated using the formula:

T = 2π√(L/g)

Where: - T = period of oscillation - L = length of the pendulum - g = acceleration due to gravity

Given that the period of oscillation of the pendulum is 1 second when it is initially displaced by 20 cm, we can use this information to calculate the period when it is initially displaced by 5 cm.

Using the formula, we can calculate the length of the pendulum (L) and then use it to find the period of oscillation when initially displaced by 5 cm.

First, let's calculate the length of the pendulum when it is initially displaced by 20 cm.

Calculation of Length (L) Using the formula: T = 2π√(L/g)

We can rearrange the formula to solve for L: L = (T/2π)^2 * g

Substituting the given values: T = 1 second g = 9.8 m/s^2

L = (1/2π)^2 * 9.8 L ≈ 0.25 m

Now that we have the length of the pendulum, we can calculate the period of oscillation when it is initially displaced by 5 cm.

Calculation of Period of Oscillation Using the formula: T = 2π√(L/g)

Substituting the calculated length and the value of g: T = 2π√(0.25/9.8) T ≈ 2π√(0.0255) T ≈ 2π * 0.1599 T ≈ 1.005 seconds

Therefore, the period of free oscillations of the pendulum when initially displaced by 5 cm is approximately 1.005 seconds.

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