Find the length of a simple pendulum that completes 17.0 oscillations in 35.0 s.
The period is T = t/N = 35/17 = 2.06 s.
T =2•π•sqrt(L/g),
L= T^2•g/(2• π)^2
.056 cm
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To find the length of a simple pendulum that completes a certain number of oscillations in a given time, we can use the formula:
T = 2π√(L/g)
Where T is the time period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity.
In this case, we know that the number of oscillations is 17.0 and the time taken is 35.0 seconds.
First, we need to find the time period (T) of the pendulum. The time period is the time taken for one complete oscillation. To do this, we divide the total time by the number of oscillations:
T = 35.0 s / 17.0
T ≈ 2.06 s
Now, we can rearrange the formula to solve for the length (L) of the pendulum:
L = (T^2 * g) / (4π^2)
Substituting the known values:
L = (2.06^2 * 9.8) / (4π^2)
L ≈ 0.571 meters
Therefore, the length of the simple pendulum is approximately 0.571 meters.