We're supposed to make a simple pendulum with a period of 24 seconds. So i attached a hardware bolt at the end of a string. The teacher is going the start the timer once we release the pendulum and wait until it returns to its maximum again.

In our calculations we need to show how many periods are needed to get 24 seconds precisely. But I thought 24 secs was the period..?
I calculated that I need 143.13 m of string for a period of 24 seconds. But that's for one oscillation right? Our teacher said we can use how as many oscillation as you want. So to figure out oscillations, is that just frequency (1/24 s) ?
Also, I'm not sure what formula I would use to get the angle where we have to release the pendulum.
HELP!!

To clarify, the period of a pendulum is the time it takes for one complete oscillation or swing back and forth. In this case, your teacher wants you to use a pendulum with a period of 24 seconds.

First, let's address your calculation for the length of the string. The formula for the period of a simple pendulum is given by:

T = 2π√(L/g)

Where T is the period, L is the length of the string, and g is the acceleration due to gravity. Rearranging the formula, we have:

L = (gT^2)/(4π^2)

Substituting in the values for g (approximately 9.8 m/s^2) and T (24 s), we can calculate the length of the string needed for a period of 24 seconds precisely.

L = (9.8 m/s^2 * (24 s)^2) / (4π^2) ≈ 143.13 m

So your calculation of needing 143.13 m of string for one oscillation is correct.

Now, if you want to determine the number of oscillations within the 24-second period, you can use the concept of frequency. Frequency is the number of oscillations per unit of time, and it is the reciprocal of the period. Therefore, the frequency of the pendulum would be:

f = 1 / T = 1 / 24 s ≈ 0.0417 Hz

This means the pendulum completes approximately 0.0417 oscillations per second.

To find the angle at which you should release the pendulum, you can use the relationship between the length of the string, the angle, and the maximum displacement of the pendulum. The formula is given as:

θ = sin^(-1)(d/L)

Where θ is the angle, d is the maximum displacement from the equilibrium position, and L is the length of the string.

In this case, the maximum displacement is usually considered to be when the string makes an angle of 90 degrees with the vertical.

θ = sin^(-1)(1/1) = sin^(-1)(1) ≈ 90 degrees

So you can release the pendulum at an angle of approximately 90 degrees to achieve the desired behavior.

Remember that these calculations and formulas are based on ideal conditions and may not fully reflect real-world scenarios, but they provide a good starting point for your experiment.