(Solved): Find the system's natural frequency. 4. A steel shaft is fixed at one end and carries a steel disc ...

Find the system's natural frequency.

4. A steel shaft is fixed at one end and carries a steel disc at the other end as shown below. We want to find the system's natural frequency of torsional vibration, where \( d=0.05 \mathrm{~m}, l=2 \mathrm{~m}, D=1 \mathrm{~m} \), and \( h=0.1 \mathrm{~m} \). Assume the mass of the disk \( m=600 \mathrm{~kg} \). (b) (a) Find the equivalent torsional spring constant. Refer to the formulas on the front pages of the textbook. Use \( G=79.3 \mathrm{GPa} \). (b) The equation of motion of the torsional system is given by \[ J_{0} \ddot{\theta}+k_{t} \theta=0 \]