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6 Free Vibration of Multiple Degrees of Freedom System
6.7 A massless cantilever beam of length L supports two lumped masses mL/2 and
mL/4 at the midpoint and free end as shown in the figure (a). The degrees of
freedom and applied forces are shown in figure (b). Formulate the equations
of motion of the system.
6.8 The fundamental frequency of a uniform cantilever beam of mass M and
length L is 3.515
E I /Ml 3 . If a lumped mass m 0 is attached to the beam at
a distance L/3 from the fixed end, determine the new fundamental frequency.
6.9 Determine the natural frequencies and modes of the system shown in the
figure
6.10 Determine the natural frequencies and modes for the system of figure (Prob.
6.4). Show that the modes satisfy orthogonality properties.
6 Free Vibration of Multiple Degrees of Freedom System
6.7 A massless cantilever beam of length L supports two lumped masses mL/2 and
mL/4 at the midpoint and free end as shown in the figure (a). The degrees of
freedom and applied forces are shown in figure (b). Formulate the equations
of motion of the system.
6.8 The fundamental frequency of a uniform cantilever beam of mass M and
length L is 3.515
E I /Ml 3 . If a lumped mass m 0 is attached to the beam at
a distance L/3 from the fixed end, determine the new fundamental frequency.
6.9 Determine the natural frequencies and modes of the system shown in the
figure
6.10 Determine the natural frequencies and modes for the system of figure (Prob.
6.4). Show that the modes satisfy orthogonality properties.