The system in the figure below consists of a massless spring with stiffness 60 N/m and unstretched length 0.6 m that is wrapped around a rigid vertical bar. A collar C of mass 6 kg is attached to the end of the spring and slides without friction along the vertical bar. A second rigid massless bar of length 0.5 m is attached to the collar and pivots without friction about its attachment point. A particle P of mass 1 kg is rigidly attached to the end of the second bar. Take as generalised coordinate q₁ the vertical coordinate of C and as generalised coordinate q2 the angle of the second bar with respect to the vertical bar. www. a) Derive expressions for the position an velocity vectors of the mass in terms of the generalised coordinates 9₁ and 92 and their derivatives. b) Determine the kinetic energy, potential energy and Lagrange functions of the system. Determine the Euler-Lagrange equations of the system.
The system in the figure below consists of a massless spring with stiffness 60 N/m and unstretched length 0.6 m that is wrapped around a rigid vertical bar. A collar C of mass 6 kg is attached to the end of the spring and slides without friction along the vertical bar. A second rigid massless bar of length 0.5 m is attached to the collar and pivots without friction about its attachment point. A particle P of mass 1 kg is rigidly attached to the end of the second bar. Take as generalised coordinate q₁ the vertical coordinate of C and as generalised coordinate q2 the angle of the second bar with respect to the vertical bar. www. a) Derive expressions for the position an velocity vectors of the mass in terms of the generalised coordinates 9₁ and 92 and their derivatives. b) Determine the kinetic energy, potential energy and Lagrange functions of the system. Determine the Euler-Lagrange equations of the system.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:The system in the figure below consists of a
massless spring with stiffness 60 N/m and
unstretched length 0.6 m that is wrapped
around a rigid vertical bar. A collar C of mass
6 kg is attached to the end of the spring and
slides without friction along the vertical bar. A
second rigid massless bar of length 0.5 m is
attached to the collar and pivots without
friction about its attachment point. A particle
P of mass 1 kg is rigidly attached to the end
of the second bar. Take as generalised
coordinate q₁ the vertical coordinate of C
and as generalised coordinate q2 the angle of
the second bar with respect to the vertical bar.
www
92
P
a)
Derive expressions for the position an
velocity vectors of the mass in terms of the
generalised coordinates q₁ and q2 and
their derivatives.
b)
Determine the kinetic energy, potential
energy and Lagrange functions of the
system.
c)
Determine the Euler-Lagrange equations of
the system.
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