Your boss at the cut-rate cuckoo clock company asks you whatwould happen to the frequency of the angular shm of the balancewheel if it had the same density and the same coil spring (thus thesame torsion constant), but all the balance wheel dimensions weremade one-third as great to save material.

a)by what factor would the frequency change?

b)would the frequency increase or decrease by the factor foundin part (a)?

c)by what factor would the torsion constant need to be changedto make the smaller balance wheel oscillate at the originalfrequency?

d)would the torsion constant need to be increased or decreasedby the factor found in part (c)?