Mass Reflectance

In the mass-string-collision problem, we can immediately write down the force reflectance of the mass:

$$\hat{\rho}(s) = \frac{R_{\mbox{mass+string}}-R_{\mbox{string}}}{R... ...string}}+R_{\mbox{string}}} = \frac{(ms+R) - R}{(ms+R) + R} = \frac{ms}{ms+2R}$$

The velocity reflectance is simply $-\hat{\rho}(s)$, since

$$\hat{\rho}(s) \isdef \frac{F^{-}}{F^{+}} = \frac{-RV^{-}}{RV^{+}} = - \frac{V^{-}}{V^{+}}$$

• Simplified impedance analysis is a nice shortcut
• Be careful to correctly identify the impedance jump