Question
Can you please help me with these questions
From the theory section of the lab we have two ways to determine the angular frequency omega of oscillations of the mass m: omega = 2pi/T and omega = Both ways to determine angular frequency omega must give the same value. Equate the above equations and solve for T2. The result in part (a) should look like the standard equation for a straight line y = mx + b if the variable for the x-axis is taken to be the mass m (do a little rearranging if needed). This means if we plot T2 vs. m we would see a straight line. Compare the standard form of the equation for a straight line and the result for part (a) and determine the theoretical value for the slope in terms of constants and the dynamical spring constant kd. In terms of the slope (and other constants), what is the value of the dynamical spring constant kd? Again, compare the standard form of the equation for a straight line and the result for part (a), what should the theoretical value for the y-intercept be in terms of constants and the dynamical spring constant kd and m0 the effective mass of the spring? In terms of the y-intercept (and other known values), what is the value of the effective mass of the spring m0?
Explanation / Answer
2 pi/T = sqrt(k/(m + m0))
4 pi^2/T^2 = k/(m+m0)
T^2/4 pi^2 = m/k + m0/k
T^2 = 4 pi^2/k m + 4 pi^2 m0 /k
b) slope is 4 pi^2/k
c) intercept is 4 pi^2 m0/k