Calculating Theoretical Time with the T = 2 (pie) Formula

[SS2006]

we got this formula

T = 2 (pie) times square root of m/k

the lab says that formula will get us theoreitcal time

in the lab itself tho, it says we should choose a appropriate time and se ehow many tiems the spring will occlilate in this time period, we chose 20 seconds

our data was as follows

100 Grams = 48 osccilations in 20 seconds

200 grams = 37 oscilations in 20 seconds
and so on..

how do i translate this info into the formula, it says we should get similar results from the formula and from our own lab work. our spring constant we used was the same one we got from ou rprevou slab (where we had to acutally fidn the spring constant) and it was 25 n/m

so can someoen tell me, what do i do, in the formula do i use 200 grams or 0.2 kg, and the 48 oscilaions in 20 seconds, am i supposed to find out how many it is supposed to be in 1 seconds, and compare it to whatever the formula gives me. I just want you guys to chcek it out and se eif it works, i don't now wha tnumbers to use. some help pelase :)

 

[Physics Monkey]

Your theoretical period (time to make one oscillation) is T = 2 \pi \sqrt{m/k}, right? You expect that your data will reproduce this formula to within some error. For each data set, you can calculate the period and you know the mass and the spring constant, so you can compare both sides of the equation and see if they match up. To get the period you should think about how many oscillations will be made in 20 sec for each mass. Since you know how many oscillations were made, you can solve for the period. When computing the theoretical period, all you need to do is make sure your units match up. If k is in N/m then m had better be in kg.

 

[andrevdh]

I think what is meant by "should get similar results" is that you should get the same force constant for the spring which is done as follows:
Calculate the period of oscillation for each mass and square it. Plot a graph of this value against the mass. According to the theory your formula for the graph is:
T^2=\frac{4\pi^2}{k}m
the gradient of such graph is therefore
\frac{4\pi^2}{k}
which enables you to determine the force constant.