Methink the qn and ans given to problem ( 6 ) are also self- cotradictory !!
It is said that the mass of the wheels are negligble .
Then how in the total energy expression of the system can a rotational energy term possibly occur ?
On the other hand consider a wheel of mass M be attached to the end of the spring . If u carry out the analysis u will find that

is indeed greater than sqrt( k/m ) .
Plz explain it also .