Answer to Question #145429 in Classical Mechanics for alwande hadebe

Question

simple pendulum consisting of a point mass m on a massless string of length l
attached to the ceiling of a room is oscillating in a plane in the earth gravitational
field.
a) Write down D’Alembert’s equation in cartesian coordinates.
b) Find the constraint of the system and classify it according to holonomic/non-
holonomic and skleronomic/rheonomic.
c) Express the cartesian coordinates of the point mass in appropriate generalized
coordinates. What is the number of degrees of freedom of the point mass?
d) Express the virtual displacements δx and δy in terms of independent general-
ized coordinates.
e) Derive the equations of motion based on D’Alembert’s equation.
f) Solve the equation of motion for small oscillation angles.

Answer 1

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