Pendulum investigation with a stop

[exequor]

I did this experiment with various values for (d), which is the height from the top of the string to the stop. The length of the string was 0.7m. Since i used 6 differnt values for (d) i got 6 readings.

why i stated all this is because i have to find g from the following expression


$$T = \frac{-\pi^2}{g} (\frac{d}{T}) + 2\Pi \sqrt{\frac {l}{g}}$$

I have tried lots of variations but i just can't find anything close to 9.8m/s^2.

what i did was i tried a single set of results like:
d = 0.5m
T = 1.31
thus d/T = 0.38
and l = 0.7m

could someone use the same and tell me what their result for g was, please.

 

[LeBrad]

I got g=9.48

If you're having trouble solving that, try transforming it into a quadratic equation. You could also move T to the right side, plot it as a function of g, and find the roots.

 

[M98Ranger]

Thank you for sharing your experiment and results with us. It seems like you have conducted a pendulum investigation with a stop and are trying to find the value of acceleration due to gravity (g) using the given expression. I understand that you have used 6 different values for (d) and have obtained 6 readings, but you are having trouble finding a result close to 9.8m/s^2.

Firstly, I would like to point out that the expression you have used is the equation for the period of a simple pendulum, which 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. In your case, you have rearranged the equation to solve for g, which is perfectly fine.

Now, coming to your specific results, if we use the values you have provided (d = 0.5m, T = 1.31s, and l = 0.7m), we can calculate the value of g using the given expression as follows:

T = (-π^2/g)(d/T) + 2π√(l/g)
1.31 = (-π^2/g)(0.38) + 2π√(0.7/g)
1.31 = (-1.18/g) + 2π√(0.7/g)
1.31 + 1.18/g = 2π√(0.7/g)
(1.31 + 1.18/g)^2 = 4π^2(0.7/g)
1.72 + 2.59/g + 1.40/g^2 = 4.38/g
1.40/g^2 + 2.59/g - 2.76/g + 1.72 = 0
1.40/g^2 + 0.83/g - 1.04 = 0

Using the quadratic formula, we get two possible values for g: 3.89m/s^2 or -0.60m/s^2. However, we know that the value of acceleration due to gravity cannot be negative, so we can discard the second result.

Therefore, using your given values, the calculated value of g is 3.89m/s^2. This is quite far from the expected value