Calculate the length of a displaced pendulum Bob which pass through its lowest point twice every second. Take g=10m/s²
it passes a point once every second
... so the period is 2 seconds
period = 2 π √(length / g)
2 = 2 π √(L / 10) ... L = 10 / π^2
To calculate the length of a displaced pendulum bob that passes through its lowest point twice every second, we can use the formula for the period of a pendulum.
The period of a pendulum can be calculated using the formula:
T = 2π√(L/g)
Where:
T = Period
L = Length of the pendulum
g = Acceleration due to gravity (10 m/s², in this case)
We are given that the pendulum passes through its lowest point twice every second. This means that the time taken for one complete oscillation (from one extreme to another and back) is 1 second.
Since the period (T) is the time taken for one complete oscillation, we have T = 1 second.
Now, let's substitute the known values into the formula and solve for the length of the pendulum (L):
1 = 2π√(L/10)
We can start by isolating the term containing L:
1/2π = √(L/10)
Next, square both sides of the equation to eliminate the square root:
(1/2π)² = L/10
1/4π² = L/10
To solve for L, multiply both sides of the equation by 10:
10/4π² = L
2.53 meters (rounded to two decimal places) = L
Therefore, the length of the displaced pendulum bob is approximately 2.53 meters.
To calculate the length of a displaced pendulum bob, we need to use the formula for the period of a pendulum.
The period (T) of a pendulum is the time it takes to complete one full swing back and forth. In this case, the bob passes through its lowest point twice every second, so the period is 1/2 seconds.
The formula for the period of a pendulum is:
T = 2π√(L/g),
where L is the length of the pendulum and g is the acceleration due to gravity.
Given that g = 10 m/s² and T = 1/2 seconds, we can rearrange the formula to solve for L:
L = (T² * g) / (4π²).
Substituting the values, we have:
L = ((1/2)² * 10) / (4 * π²),
L = (1/4 * 10) / (4 * π²),
L = 2.5 / (4 * 9.87),
L ≈ 0.0803 meters.
Therefore, the length of the displaced pendulum bob is approximately 0.0803 meters.