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# Physics/Simple Harmonic Motion

Question
A hovering fair-sized insect rises a little during the downstroke of its wings and essentially free-falls during the upstroke.  The end result is that the creature oscillates in midair. Assume it typically falls about .212 mm per cycle. What is the wingbeat period?

If we assume that the insect falls 0.212mm=0.000212m using kinematics the time to fall can be determined from:
Df=1/2*a*t^2
0.000212=9.8/2*t-^2
Solving for t:
t=sqrt(0.000212/4.9)=0.00658sec
If we assume that approximately the same time is required to return the insect to the initial height we would need to double this time to find the period:
T=2*t=2*--0.00658sec=0.0131sec
By the way, in any case this is NOT simple harmonic motion. For it to be so there would have to be an equilibrium position, which there is not, and the restoring force from equilibrium would need to be proportional to the displacement from equilibrium. According to this problems statement the force accelerating the bug downward is gravity which is constant.

Physics