Problem B Consider the spring-mass system whose motion is governed by the differential equation: 4y" 43y +2y=10cos(wt) , w>0 where y is the displacement from equilibrium in cm and t is the time in seconds. 1. Find the amplitude R = R(w) of the particular solution (steady-state response), y,, = R cos(wt &) , for this system in terms of the forcing frequency w . Use the formula sheet from class (or equation (11) and (12) Sect. 3.8 in your text) to solve this problem. 2. Use a graphing tool to plot the function R = R(w) you found in question 1. Use the graphing tool to find the maximum value R,,,, of the amplitude of the particular solution (steady-state response) for this system and the frequency @, for which it occurs. max 3. Use the formula sheet from class (or equation (14) and (15) Sect. 3.8 in your text) to find R,,,,, and the frequency @, for which it occurs. Confirm that these values are the same as the values you found graphically in question 2. 4. Figure 3.8.2 in your text uses dimensionless parameters to illustrate the behavior of spring-mass systems such as the one given in this problem. After reviewing the graph in Figure 3.8.2 and reading the discussion in the text, briefly describe key features of spring-mass systems illustrated in Figure 3.8.2. \f72 max = W = 02 1 - 2m2 O (14) 2mk Wmax