To determine the natural frequencies of the given beam and plot their shapes. Check the orthogonality condition. Draw the final moments resulting from inertial forces (assume the excitation frequency as the arithmetic mean of the previously calculated natural frequencies, i.e. \( \theta=\frac{\omega_1+\omega_2}{2} \) ) \( \text{Data:} \ EI= 2.1 \cdot 10^5 \ kNm^2, \ m=200 \ kg, \ P=10\cdot sin(\theta \ t) \)

To determine the inertial forces for the given frame. Given: \( \ EI= 4000 \ kNm^2, \ m=700 \ kg, \ P=25 \ sin(pt), \ p=15 \ \frac{rad}{s} \)

To draw the ultimate moments resulting from inertial forces for the given frame. Draw the envelope of moments. Data: \( \mathrm{E}=2.1 \cdot 10^{11} \frac{\mathrm{N}}{\mathrm{m}^2} \), \( \mathrm{~m}=660 \mathrm{~kg} \), \( \mathrm{~m}_{\mathrm{w}}=2250 \mathrm{~kg} \), \( \mathrm{e}=4.3 \mathrm{~mm} \), \( \mathrm{n}=470 \frac{\mathrm{rev}}{\mathrm{min}} \), IPN 200 beam cross-section.

To draw the final moments caused by inertial forces for the given frame and to draw the envelope of moments. Data: \( \mathrm{E}=2.1 \times 10^{11} \frac{\mathrm{N}}{\mathrm{m}^2}, \mathrm{~m}=680 \mathrm{~kg}, \mathrm{~m}_{\mathrm{w}}=400 \mathrm{~kg}, \mathrm{e}=2 \mathrm{~mm}, \mathrm{n}=300 \frac{\mathrm{rpm}}{\mathrm{min}} \), cross-section of the frame with the moment of inertia \(I=4250\ cm^4 \).

To draw the ultimate moments resulting from inertia forces for the given frame. Data: \( \theta =0.8\cdot \omega_1 \, F_0=2\ kN \)

To draw the final moments caused by inertia forces for the given frame. Check if the stresses in the rod with a rectangular cross-section of 12 x 24 cm and a Young's modulus of 210 GPa do not exceed the allowable strength of 240 MPa. Data: \( \mathrm{p}=8.25 \frac{\mathrm{rad}}{\mathrm{s}}, \mathrm{m}=2.75 \mathrm{t}, \mathrm{P}=20.5 \mathrm{kN} \)