Problem 3 Consider an infinite string of tension T and density p which has a small bead of mass M attached to it. (a) Find the transmission and reflection coefficients for the bead for incident waves of frequency w from the left. (b) Now assume the bead is a damped oscillator: it is connected to a spring of zero length and spring constant k, and is acted by a resistive force of -bu. What changes for the sum of the reflection and transition coeffi- cients compared to part (a), why? How do the coefficients behave at the resonance