17. Periodic Motion

The historic first playground on Mars has just opened. A child is on a swing with chains of length $2.3\mathrm{m}.$ If a parent pulls the child backward $$ from equilibrium, what is the child's maximum speed? The acceleration due to gravity on Mars is $3.7{\text{m/s}}^2$.

A 20 kg child is on a swing that has chains $2.4\mathrm{m}$ long. Being interested in physics, the child's father gives a push and then watches to see what happens. He notices that the amplitude of the child's oscillation decreases by half in 20 s. What is the value of the time constant?

A 20 kg child is on a swing that has chains $2.4\mathrm{m}$ long. At what frequency should the child's father deliver his pushes to ensure the highest swing possible?