A pendulum makes 120 complete oscillations in 3.00 minutes at a location where g= 9.98m/s^2
Find the period of the period
Find the length
I tried using the 2pi sqrt. L/g formula
I don't know why I got this huge number
The period P is 3/120 = 1/40 minute = 1.5 seconds.
P = 2*pi*sqrt(L/g) = 1.5 s
sqrt(L/g) = 0.2387
L/g = 0.05699
L = 0.569 m
That doesn't seem very huge to me.
Where did you derive 0.2387 ?
To find the period of the pendulum, we can use the formula T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
Given that the pendulum makes 120 complete oscillations in 3.00 minutes, we can calculate the period by dividing the total time by the number of oscillations:
T = Total time / Number of oscillations
T = 3.00 min / 120
First, let's convert the time to seconds:
T = 3.00 min * 60 s/min / 120
T = 180 s / 120
T = 1.5 s
We have now found the period of the pendulum to be 1.5 seconds.
To find the length of the pendulum, we rearrange the formula T = 2π√(L/g) to solve for L:
L = (T^2 * g) / (4π^2)
Substituting the known values:
L = (1.5^2 * 9.98) / (4π^2)
Using a calculator, we can evaluate this expression:
L ≈ 3.74 m
Therefore, the length of the pendulum is approximately 3.74 meters.
To find the period of the pendulum, you can use the formula:
T = 2π√(L/g)
where T is the period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity.
Given that in this case, the pendulum makes 120 complete oscillations in 3.00 minutes, you can first calculate the number of oscillations per second:
Number of oscillations = 120 oscillations
Time = 3.00 minutes = 3.00 * 60 = 180 seconds
Number of oscillations per second = 120 oscillations / 180 seconds = 2/3 oscillations/second
Now, since the period is the time taken for one complete oscillation, the period (T) can be calculated as the inverse of the number of oscillations per second:
T = 1 / (2/3) = 3/2 seconds
This is the period of the pendulum.
To find the length (L) of the pendulum, you can rearrange the formula as follows:
L = (T^2 * g) / (4π^2)
Plugging in the values:
L = ((3/2)^2 * 9.98) / (4π^2)
L ≈ 0.115 m
Therefore, the period of the pendulum is 3/2 seconds and the length of the pendulum is approximately 0.115 meters.