Consider a pendulum of mass “m" attached to a spring of mass "M" that is free to move in single dimension along a frictionless horizontal surface. Take the gravity g = 10 m/s² and the gravitational potential energy is equal to zero at the level of block (y = 0).
Consider a pendulum of mass “m" attached to a spring of mass "M" that is free to move in single dimension along a frictionless horizontal surface. Take the gravity g = 10 m/s² and the gravitational potential energy is equal to zero at the level of block (y = 0).
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:Consider a pendulum of mass “m" attached to a spring of mass “M" that is free to move in
single dimension along a frictionless horizontal surface. Take the gravity g = 10 m/s² and the
gravitational potential energy is equal to zero at the level of block (y = 0).
X
Datum of potential energy: PE = 0
m
a) Write the equations of constraints.
b) Determine the degree of freedom (S = ??)
c) Write the expression of ry as a function of X and unit vector i
d) Write the expression of r'm as a function of unit vector i, e', and e',
e) Find the expression of kinetic energy of the system as a function of (M, m, X, I, 0,0)
f) Write the expression of potential energy PE of the system as a function of (m, l, 0)
g) Write the Lagrangian equation
h) Deduce the equations of motion from Euler-Lagrange equations
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