Numerical investigation of symmetric and asymmetric periodic oscillations

Global information for the periodic solutions — symmetric and asymmetric — of the ‘gravitational’ spring-pendulum problem is given for the first time. For two different sets of the parameters of this problem, the families of symmetric periodic solutions which emanate from the equilibrium point have been determined. Further families of asymmetric and symmetric solutions which bifurcate from them have also been examined and interesting results for their behaviour have been pointed out.