Question

Период колебаний математического маятника равен 2 с.При какой длине нити период колебаний будет в четыре раза больше? формула и решение надо помогите пожалуйста

Answer 1

Период колебаний математического маятника $T=2 \pi \sqrt{ \frac{l}{g} }$
Чтобы Увеличить период колебаний в четыре раза нужно увеличить длину нити в 16 раз, 16 из под корня выйдет и получится 4

Answer 2

Calculation of the Period of a Simple Pendulum

The period of a simple pendulum is the time it takes for the pendulum to complete one full oscillation, or swing, back and forth. The period can be calculated using the formula:

T = 2π√(L/g)

Where: - T is the period of the pendulum, - L is the length of the pendulum's string or rod, - g is the acceleration due to gravity.

In this case, we are given that the period of the pendulum is 2 seconds. We need to find the length of the pendulum's string when the period is four times longer.

Solution

Let's assume the original length of the pendulum's string is L1. According to the given information, the period of the pendulum is 2 seconds when the length of the string is L1.

We need to find the length of the string when the period is four times longer, which means the new period is 8 seconds.

Using the formula for the period of a simple pendulum, we can set up the following equation:

8 = 2π√(L2/g)

To solve for L2, we can rearrange the equation as follows:

L2 = (8^2 * g) / (4π^2)

Now, let's substitute the value of g (acceleration due to gravity) into the equation. The approximate value of g is 9.8 m/s^2.

L2 = (8^2 * 9.8) / (4π^2)

Calculating this expression will give us the length of the pendulum's string when the period is four times longer.

Calculation

L2 = (64 * 9.8) / (4π^2)

Using a calculator, we can find the approximate value of L2.

L2 ≈ 1.01 meters

Therefore, when the length of the pendulum's string is approximately 1.01 meters, the period of the pendulum will be four times longer, or 8 seconds.

Please note that the above calculation assumes a simple pendulum with negligible air resistance and small oscillations.