9.11 Introduction to the Famous Scientists
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O
x
y
c
C
l
P
Problem 9.3 The deflection of the simple beam subjected to the concentrated load
O
x
y
l
q
Problem 9.4 The deflection of the clamped beam subjected to the uniform load
Hint: According to the theory of differential geometry, the surface area of the
film in the deformation condition is
A =
¨
S
1 + w 2
x + w 2
y dxdy
9.9 As shown in Problem 9.5, the spring of stiffness k hangs an object of mass m.
If the suspension point vertically moves in accordance with the law of S =
a sin ωt, using the Lagrange’s equation to establish the differential equation
describing the object motion; If the object of the suspension point begins to
move at the static equilibrium position, solve the equation.
9.10 Let the simple beam bear the distributed load of strength q, using the Hamilton’s
principle to derive the differential equation of lateral free vibration of the beam.
9.11 As shown in Problem 9.6, the two objects of mass m 1 and m 2 are connected in
series with two springs that the elastic coefficients are k 1 and k 2 respectively,
they are hung at fixed-point O, constitute a particle system, the spring mass