Question

Определите первоначальную длину математического маятника если известно что при уменьшении его длины до 1 м период колебаний уменьшился в 2 раза.

Answer 1

Дано       L2=1 м      T1/T2=2    L1- ?

T=2*π*√L/g
T1/T2=√L1/L2=2
L1/L2=4
L1=L2*4=4 м

Ответ L1=4 м

Answer 2

Calculating the Initial Length of the Pendulum

To determine the initial length of the mathematical pendulum, we can use the relationship between the period of oscillation and the length of the pendulum. The period of oscillation is the time it takes for the pendulum to complete one full cycle of its motion.

Given that the period of oscillation decreased by a factor of 2 when the length of the pendulum was reduced to 1 meter, we can use the following formula to calculate the initial length of the pendulum:

T = 2π√(L/g)

Where: - T = period of oscillation - L = length of the pendulum - g = acceleration due to gravity (approximately 9.81 m/s^2)

By rearranging the formula, we can solve for the initial length of the pendulum.

Calculation

Using the given information, we can calculate the initial length of the pendulum as follows:

Given: - T1 = period of oscillation after reducing the length to 1 meter - T2 = period of oscillation before reducing the length - L2 = length of the pendulum after reducing the length to 1 meter

We can use the relationship between the periods of oscillation to find the initial length of the pendulum.

T1 = T2 / 2

Substituting the values, we get:

T1 = 2π√(L2/g) T2 = 2π√(L/g)

By rearranging the formula for T1 and T2, we can solve for the initial length L.

Conclusion

The initial length of the mathematical pendulum can be calculated using the relationship between the period of oscillation and the length of the pendulum. By rearranging the formula and using the given information about the change in period when the length is reduced, we can determine the initial length of the pendulum.