Problem M1 The system in the figure consists of four identical springs of spring constant k = 50 N/m and negligible length at rest. The four spring ends are constrained in a horizontal plane. The other ends are connected to a material point of mass m = 50 g. With reference to the Cartesian coordinate system shown in the figure, the four endpoints are located at the points P₁ = (L, 0, 0), P₂ = (0, L, 0), P, = (-L, 0, 0) and P₁ = (0, -L, 0), with L= 20 cm. The system is in the absence of gravity. a) The material point is initially stationary at the point P(0, 0, L). Calculate the modulus of the velocity when it passes through the origin. b) With reference to the previous question, qualitatively describe the motion of the point and calculate its period. + c) Now consider the case in which the material point is constrained to move in the horizontal plane. Calculate the potential energy of the point material as a function of distance from the origin and determine its value if that distance is 2L.
