From the theory section of the lab we have two ways to determine the period of o
ID: 1893895 • Letter: F
Question
From the theory section of the lab we have two ways to determine the period of oscillations ofthe mass m:
? = 2p/T and
? = vkd/m+m0
a. (5 points) Both ways to determine ? 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.
b. ( 5 points) 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?
c. (5 points) 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
(a) Given ? = 2p/T and ? = v(kd/m+m0). => 2p/T = vkd/m+m0 => T/2p = v(m+m0/kd) => T2/4p2 = m+m0/kd => T2 = [4p2/kd][m+m0] ---------(1) which is clearly a straight line when drawn between T2 and m (b) comparing (1) with equation of a straight line y = mx + b we get slope as m = 4p2/kd where kd is the dynamical spring constant. and kd = 4p2/m kd in terms of slope. (c) the theoretical value for the y-intercept be in terms of constants is b => b = 4p2m0/kd now kd in terms of y intercept b => kd = 4p2m0/b and effective mass in terms of y intercept => m0 = bkd/4p2
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.