Final answer:
Mechanical energy is conserved in a system when work is done by conservative forces such as gravitational or elastic forces, which do not transform mechanical energy into other forms such as heat, like frictional and certain magnetic forces can.
Step-by-step explanation:
Mechanical energy is conserved in the presence of certain types of forces. Specifically, gravitational and elastic forces are conservative, meaning that when these forces do work on a system, the total mechanical energy (kinetic plus potential energy) of that system remains constant, as long as there are no non-conservative forces acting, such as friction. On the other hand, frictional forces are non-conservative and dissipate mechanical energy as heat. Similarly, magnetic forces can do work on a system and the effect on mechanical energy conservation will depend on the particulars of the interaction, so without more context, it is not clear whether mechanical energy would be conserved. Therefore, gravitational and elastic forces are types of forces in which mechanical energy is conserved.