Answer Happy

** Reduced Mass. (a) If we attach two blocks that have masses mi and m2 to either end of a spring that has a force constant k and set them into oscillation by re- leasing them from rest with the spring stretched, show that the oscillation frequency is given by W = klu, where u = mim2/(mı + m2) is the reduced mass of the system. Hint: First consider the separate motions of these two blocks and write their equation of mo- tions as follows d²x1 mi =-K(X1-x2) dt2 d2x2 m2 =-k(x2-xı), dt2 from which you can obtain the two equations which describe their relative displacement Xi - X2 (SHM) and their center of mass Xcom (free motion), respectively. (b) In one of your chemistry labs, you determine that one of the vibrational modes of the HCL molecule has a frequency of f = w/(2T) = 8.97 1013 Hz. Using the result of Part (a), find the "effective spring constant" between the H atom and the CI atom in the HCI molecule. Answers: k=514 N/m