Dynamics 2e 2059
Computation.
Substituting the kinematics relations into the force laws and then substituting the force laws
into Eqs. (1) and (2), we obtain
ok1
o
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Problem 9.80
A ring of mass
m
is attached by two linear elastic cords to the
vertical supports as shown. The cords have elastic constant
k
and unstretched length
L0< L
. Assuming that the pretension in
the cords is large enough that the deflection of the cords due to
the ring’s weight can be neglected, find the nonlinear equation of
motion for the mass m.
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Dynamics 2e 2061
Problem 9.81
A ring of mass
m
is attached by two linear elastic cords to the
vertical supports as shown. The cords have elastic constant
k
and
unstretched length
L0< L
. Assuming that the pretension in the
cords is large enough that the deflection of the cords due to the
ring’s weight can be neglected, use Newton’s second law to find
the linearized equation of motion about
yD0
for the mass
m
. In
addition, determine the natural frequency of the ring’s vibration.
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permission of McGraw-Hill, is prohibited.
The natural frequency of the ring’s vibration is given by !nDpkeq=meq, and so we can write
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 2063
Problem 9.82
Solve Prob. 9.81 by finding the linearized equations of motion
using the energy method.
TD1
2mv2
y;
where vyis the speed of the ring.
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permission of McGraw-Hill, is prohibited.
Computation.
Notice that the first term in
V
is a constant and so we can ignore it when applying the energy
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