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3 For the mechanical system shown, the uniform rigid bar has mass m and is pinned at point O. For this system, use ?? as the motion variable. a) Use Rayleigh's Method to determine the natural frequency of the system (neglecting the damping). b) Use Lagrange's Equation (or Newton's Laws) to derive the equation of motion of the system. c) Using m = 1.50 kg, l = 45 cm, c = 0.125 N/(m/s), k = 250 N/m, find the angular displacement of the bar ?(t) for the following initial conditions: ?(0) = 0, ?(0) = 10 rad/s . Hint: It might be easier to write some of the quantities in terms of x or y first, then substitute in the relationships between x and y and ?.

          3 For the mechanical system shown, the uniform rigid bar has mass m and is pinned at point O. For this system, use ?? as the motion variable.
a) Use Rayleigh's Method to determine the natural frequency of the system (neglecting the damping).
b) Use Lagrange's Equation (or Newton's Laws) to derive the equation of motion of the system.
c) Using m = 1.50 kg, l = 45 cm, c = 0.125 N/(m/s), k = 250 N/m, find the angular displacement of the bar ?(t) for the following initial conditions: ?(0) = 0, ?(0) = 10 rad/s .
Hint: It might be easier to write some of the quantities in terms of x or y first, then substitute in the relationships between x and y and ?.

3 For the mechanical system shown, the uniform rigid bar has mass m and is pinned at point O. For this system, use ?? as the motion variable.
a) Use Rayleigh's Method to determine the natural frequency of the system (neglecting the damping).
b) Use Lagrange's Equation (or Newton's Laws) to derive the equation of motion of the system.
c) Using m = 1.50 kg, l = 45 cm, c = 0.125 N/(m/s), k = 250 N/m, find the angular displacement of the bar ?(t) for the following initial conditions: ?(0) = 0, ?(0) = 10 rad/s .
Hint: It might be easier to write some of the quantities in terms of x or y first, then substitute in the relationships between x and y and ?.

Added by Glenn W.

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