Using the relativistic expression for force, devise a force for which the equation of motion has an exact solution of the form x(t) = A sin(wt). a) Since the expression for the coordinater is written in terms of the coordinate time t, the proper time in the relativistic force relation will have to be transformed to the coordinate time. b) Write the Lorentz factors y in the equation of motion in terms of the total energy and the potential energy V(x). c) In order to achieve the desired form for x(t) the negative gradient of the potential should have the same form as Hooke's law. Answer F(x) = V = -m² (1– w² (A² – x²) /c²)¯/² .

Using the relativistic expression for force, devise a force for which the equation of motion has an exact solution of the form x(t) = A sin(wt). a) Since the expression for the coordinater is written in terms of the coordinate time t, the proper time in the relativistic force relation will have to be transformed to the coordinate time. b) Write the Lorentz factors y in the equation of motion in terms of the total energy and the potential energy V(x). c) In order to achieve the desired form for x(t) the negative gradient of the potential should have the same form as Hooke's law. Answer F(x) = V = -m² (1– w² (A² – x²) /c²)¯/² .