Questions ? figure \( Q 7 \) shows an approximation of a 4 cylinder engine and flywheel coupled to a propeller. They are approximated to a 3 rotor system in which the engine is equivalent to a rotor of moment of inertia \( 850 \mathrm{kgm}^{2} \), the flywheel to a second rotor of \( 370 \mathrm{kgm}^{2} \) and the propeller to a thind rotor of \( 40 \mathrm{kgm} \). The first and the second rotors are being connected by \( 50 \mathrm{~mm} \) diameter and Imeter long shaft The third rotor is connected to the second rotor by a \( 25 \mathrm{~mm} \) diameter and 2 meter long shaft as shown in figure Q7. The modulus of rigidity of the shaft is \( 80 \mathrm{GN} / \mathrm{m}^{2} \). Assuming the inertia of the shatt is negligible: a) Natural ficquencies of torsional vibrations and (10 Marks) b) The positions of the nodes. (10 Marks)

Questions 7 Figure Q7 shows an approximation of a 4 cylinder engine and flywheel coupled to a propeller. They are approximated to a 3 rotor system in which the engine is equivalent to a rotor of moment of inertia 850kgm2, the flywheel to a second rotor of 370kgm2 and the propeller to a third rotor of 40kgm2. The first and the second rotors are being connected by 50mm diameter and 2meter long shaft. The third rotor is connected to the second rotor by a 25mm diameter and 2 meter long shaft as shown in figure Q7. The modulus of rigidity of the shaft is 80GN/m2. Assuming the inertia of the shaft is negligible: a) Natural frequencies of torsional vibrations and (10 Marks) b) The positions of the nodes. (10 Marks)