A certain molecule is made up of four atoms. Three of themhave mass M and are located at the vertices of an equilateraltriangle of side a. The fourth atom has mass m and is free to movealong a line perpendicular to the triangle and passing through itscenter. Assume this atom is attracted to the other atoms by a forceproportional to the distance between them. (You can imagine theatom of mass m is attached by 3 springs of force constant k to theatoms of mass M.) Determine the Lagrangian for the system.