Amachine, modeled as a simple spring-mass system, oscillates in simple harmonic motion. its acceleration is measured to have an amplitude of 5,000 mm/s with a fre- quency of 10 hz. compute the maximum displacement the machine undergoes during this oscillation.

Apalm springs golf course has requested a permit to install a 40000 f t2 pond to enhance the beauty of its facilities. since the evaporation rates are very high in palm springs, it is likely they will need to pump a lot of groundwater to keep the pond full. the city has hired you (a water resources engineer) to determine how much water needs to be pumped per year in order to keep the pond filled. there is a small creek that discharges an average of 0.25 m3/s into the pond. the outlet valve from the pond releases an average rate of 0.30 m3/s (to keep the pond from getting stagnant). precipitation on the pond is 260 mm/year, and the annual evaporation is estimated to be 105 inches/year. the pond will be lined with concrete to prevent any drainage or seepage from the bottom. using a water balance, what volume (on average) of groundwater (in cubic meters) must be added to the lake each year to keep the pond at a constant level? draw a schematic of the problem to identify the control volume and the relevant fluxes. clearly write out/define your water balance equation and variables. be careful with the units, you might want to work in m3/year or m/year.