The belt extension *s*(*t*) in the detachment region is considered to correlate closely to the friction force fluctuations associated with detachment events (bottom row in Fig. 3). Hence, *s*(*t*) can be abstracted as a saw-tooth function for both the driver (Eq. (4a)) and driven case (Eq. (4b)). The frequency of the saw-tooth function is taken as the frequency *f*_{F,de} measured in the case with small flywheel for both the driver and driven pulleys. The duty cycles (loading phase fractions) of the saw-tooth function are 2/3 and 1/3 for the driver and driven pulleys, respectively, taken in accord with the friction force fluctuations associated with detachment events. The amplitude of belt extension, *A*_{s}, cannot be defined based on our experimental data. To this end, we have determined *A*_{s} via trial-and-error method: the amplitude of the angular velocity fluctuations (*A*_{α,po}) is calculated by numerical integration of Eq. (3) (via matlab's ode45 routine), while *A*_{s} is varied until the predicted *A*_{α,po} matches the *A*_{α,po} measured with the small flywheel in both the driver and driven cases. These values are applied to the cases of no and large flywheels to see whether the model can be predictive. The expressions used to describe *s*(*t*) are
Display Formula

(4a)$st=As3fF,de4\pi t,0\u2264t\u22644\pi 3fF,deAs3\u22123fF,de2\pi t,4\pi 3fF,de\u2264t\u22642\pi fF,de$

Display Formula(4b)$st=As3fF,de2\pi t,0\u2264t\u22642\pi 3fF,deAs32\u22123fF,de4\pi t,2\pi 3fF,de\u2264t\u22642\pi fF,de$