A pendulum has a period of 2s. What chcange in its length will double the period?
Since period = 2 pi sqrt (L/g).
L must increase by a factor of 4 to double the period.
If you need to know the new or old value of L, use the formula given above.
To find the change in length that will double the period of a pendulum, we need to understand the factors affecting the period of a pendulum.
The period of a simple pendulum, the time it takes for one complete oscillation, depends on its length and the acceleration due to gravity. The formula for the period of a pendulum is:
T = 2π * √(L / g),
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
In this case, the initial period of the pendulum is 2 seconds, and we want to find the change in length that will double the period, making it 4 seconds. Let's call the initial length L₁ and the new length we want to find ΔL.
Using the formula for the period, we can set up the following equation:
2 = 2π * √(L₁ / g), (1)
4 = 2π * √((L₁ + ΔL) / g). (2)
Now, let's solve equation (2) for ΔL by squaring both sides:
16 = 4π² * ((L₁ + ΔL) / g). (3)
We can simplify equation (3) by dividing both sides by 4π² and multiplying by g:
ΔL = (16 * g) / (4π²) - L₁. (4)
Plugging in the known values, acceleration due to gravity g is approximately 9.8 m/s²:
ΔL = (16 * 9.8) / (4π²) - L₁.
Calculating the right-hand side of the equation:
ΔL ≈ 4.915 - L₁.
Therefore, the change in length needed to double the period of the pendulum is approximately 4.915 - L₁ units.