The length of a simple pendulum is 0.58 m, the pendulum bob has a mass of 285 g, and it is released at an angle of 16 degrees to the vertical.
With what frequency does it oscillate?
The period of a simple pendulum of length L with small amplitudes is
T=2π√(L/g)
Frequency is the reciprocal of period, T.
For small amplitudes, it is (approximately) not dependent on the mass nor the amplitude (angle).
For higher amplitudes, or greater accuracy, the following series expansion can be used:
T=2π√(L/g)*(1+θ²/16+11θ^4/3072+...)
which turns out to be:
1.5353 s. instead of 1.5278 s. using the simple formula.
To determine the frequency of a simple pendulum, you can use the following formula:
frequency = 1 / time period
The time period of a simple pendulum depends on its length. The formula for the time period is:
time period = 2π * √(length / g)
Where:
- π is a mathematical constant approximately equal to 3.14159
- length is the length of the pendulum in meters
- g is the acceleration due to gravity, approximately equal to 9.8 m/s²
Let's substitute the given values into the formula to find the time period of the pendulum:
length = 0.58 m
g = 9.8 m/s²
time period = 2π * √(0.58 / 9.8)
Now, we can calculate the time period using a calculator. By substituting the values into the formula, we can simplify it to:
time period ≈ 2.921 seconds
Finally, we can find the frequency by taking the reciprocal of the time period:
frequency = 1 / 2.921
Using a calculator, the frequency is approximately 0.342 Hz.
Therefore, the simple pendulum oscillates with a frequency of approximately 0.342 Hz.