a. A 0.5 kg mass attached to a linear spring, with springconstant 5 N/m and damping constant 0.2 kg/s, is initiallydisplaced 10 cm from equilibrium. (a) What is the natural frequencyof oscillation? What is its period of oscillation? How long does ittake for the amplitude to decrease to 10% of its starting value?How many oscillations have occurred in this time? What fraction ofthe initial energy remains after this time?
b. Two traveling waves with the same amplitude A, frequency f,and wavelength λ, but out of phase with each other by one quarterof a wavelength, are both traveling to the right and superpose inspace. Find the amplitude, wavelength, and frequency of theresulting wave in terms of the given symbols. Write the equation ofthe resulting traveling wave y ( x , t ).
