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/s and gravitational potential energy is equal to zero at the level of block (y = 0). y
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/s and gravitational potential energy is equal to zero at the level of block (y = 0). y
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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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![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/s and the
gravitational potential energy is equal to zero at the level of block (y= 0).
y
X
Datum of potential energy: PE = 0
e',
a) Write the equations of constraints.
b) Determine the degree of freedom (S = ??)
c) Write the expression of rM 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, I, 0)
g) Write the Lagrangian equation
h) Deduce the equations of motion from Euler-Lagrange equations](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42603fc3-895d-4be0-9d5b-4bd894f9078a%2Fbefe5c09-9d3e-4a9b-b6b2-b9384f2023e1%2Funx7g1_processed.jpeg&w=3840&q=75)
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/s and the
gravitational potential energy is equal to zero at the level of block (y= 0).
y
X
Datum of potential energy: PE = 0
e',
a) Write the equations of constraints.
b) Determine the degree of freedom (S = ??)
c) Write the expression of rM 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, I, 0)
g) Write the Lagrangian equation
h) Deduce the equations of motion from Euler-Lagrange equations
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