Question

1. Child on swing. The equation describing damped oscillations is x(t)=Ae^-((bt)/(2m))sin(wt+ø). A child of mass 16 kg wants to swing on a swing of neglible mass. The seat of the swing is 30 cm above the ground and the total height of the swing is 2 m above the ground.
   1. The child Is too young to swing themselves. How much mechanical energy is added to the child if they are pulled back by parent a distance 40 cm from the vertical?
   2. The child is now released from rest. The distance the child swings decreases by 20 cm from the vertical after the child has swung back and forth five times. How much mechanical energy has the child lost?
   3. Is mechanical energy being lost at a constant rate? Explain.
   4. If the parent wants to keep the child swinging at the same distance, the parent needs to give the child a push. If the parent pushes the child with a constant force of 10 N, how far does the parent need to push the child in order to replace the energy that is otherwise lost in the first swing?

Answer 1