With the formula T=2pi(sqrt)(m/k) how do I determine the experimental value of the spring constant using the information on the table below.
The info that I have on my table is:
Masskg Average time for 10 T(s)T^2(s^2)
vibrations
0.1 5.05 .505 .255
0.2 7.22 .722 .521
0.3 9.03 .903 .815
0.4 10.1 1.01 1.02
0.5 10.95 1.10 1.20
0.7 13.25 1.33 1.76
0.9 15.30 1.53 2.34
1.2 17.33 1.73 3.00
1.5 19.06 1.91 3.63
To determine the experimental value of the spring constant (k), you can use the equation T = 2π√(m/k), where T is the period of vibration (the average time for 10 vibrations in this case), m is the mass of the object attached to the spring, and k is the spring constant.
Using the given table, we have the values of mass (m) and the square of the period (T^2). Let's use the formula to find the experimental values of the spring constant for each mass:
For the first row with mass 0.1 kg and T^2 value of 0.255 s^2:
T = 2π√(m/k)
0.505 = 2π√(0.1/k)
Solving for k, we have:
k = (2π√(0.1))/0.505
Similarly, you can calculate the experimental value of the spring constant (k) for each row using the given values for T^2. Substitute the values of T^2 and mass (m) into the formula and solve for k using algebraic manipulations.
By performing the calculations for each row, you will get the experimental values of the spring constant for each mass in the table.