Consider a pendulum of mass "m" attached to a spring of mass "M that is free to move insingle dimension along a frictionless horizontal surface. Take the gravity g = 10 m/s and thegravitational potential energy is equal to zero at the level of block (y= 0).yXDatum of potential energy: PE = 0e',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 id) 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 equationh) Deduce the equations of motion from Euler-Lagrange equations

We know that the formula of the spring force is given as F = -kx here k is the spring constant x…

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

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter7: Work And Kinetic Energy

Section: Chapter Questions

Problem 108CP: Consider a linear spring, as in Figure 7.7(a), with mass M uniformly distributed along its length....

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Question

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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

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