a light pointer fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. 8 complete oscillations are counted when the plate falls through 10cm. What is the frequency of the fork ?

Answer 1

so the issue is how much time elapsed when it fell .1m.

d=1/2 g t^2
t=sqrt(2d/g)=sqrt(2*.1)/9.8) sec which is the time for 8 oscillations.

frequency=1/period=8/t