A linear resonant actuator (LRA) is a type of vibration actuator that is used to create vibration in a cell phone or game controller. One type of construction for such an actuator is on the right hand side of Figure 4. It's worth looking at how clever the design is in this design, the springs actually carry electrical current to the coil. And it all fits into a folded sheet metal assembly and sold for a dollar or two. These parts can be as small as 4 mm thick, 8 mm wide, and 15 mm long, and still make enough vibration to be felt through your phone. We'll talk more about them in the course. In this problem, karm and Carm represent the (effective) stiffness and damping constants of the connection of the phone to the body. This might change based on someone's grip. m, is the mass of a phone. mact is the mass of the actuator that moves, Kact is the combined stiffness of the springs inside the actuator, and eact is the damping coefficient internal to the actuator (generally very low). Because of the arrangement of the actuator, the effective force acts on both the phone and the mass, in opposite directions. The zero-displacement position of both springs is when p = act = 0. The value of the force and how the circuit part of the coil can be modeled we will consider in a future assignment. Karm HH Carm Actuator electromagnetic force Fact mp Fact Kact Cact mact Xact CHASSIS CURRENT CONDUCTING SPRINGS NOVING MASS Nov NEDOTHUM FLEX CRCUIT MAGNET AND VOICECOL PRECISION MICRODRIVES PRECISION HAPTIC Z-AXIS LINEAR RESONANT ACTUATOR Credit: Precision Microdrives, Ltd. M -FLYING LEADS FLEK CIRCUIT SELF NOHESIVE BACKING d NEODYMUM MAGNET CASE VERATING PASS ASSEMBLY https://www.precisionmicrodrives.com/vibration-motorsa/linear-resonant-actuators-iras/ Figure 4: (Left) Schematic diagram of a linear resonant actuator attached to a phone, held by a human. (Right) Internal construction of one type of LRA. Your tasks: A Draw the free body diagram for the actuator mass (mass mact). (4 pts) B Draw the free body diagram for the phone (mass m). (3 pts) C Write the equations of motion for the system with Ep and Fact, the phone position and the actuator mass position, respectively, as your dynamic variables. (8 pts)