Question: when can the toddler use the mattress as a trampoline...
When can the toddler use the mattress as a trampoline, losing contact with it for part of each bounce? Give the minimum amplitude of bouncing (in m) for this to be the case.
Assume that the child has mass 18.2kg and the mattress has stiffness 680N/m.
Hint: This will happen when the maximum acceleration of the mattress becomes greater than the acceleration due to gravity, so that at the top of the bounce the mattress starts moving down faster than the child is falling.