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).
a) Write the equations of constraints.
b) Determine the degree of freedom (S = ??)
c) Write the expression of r⃗⃗⃗M⃗ as a function of X and unit vector i
d) Write the expression of r′m

⃗⃗⃗⃗⃗⃗ as a function of unit vector i , e′r
⃗⃗⃗⃗⃗ and e′θ
⃗⃗⃗⃗⃗
e) Find the expression of kinetic energy of the system as a function of (M, m, Ẋ
, l, θ, θ̇)
f) Write the expression of potential energy PE of the system as a function of (m, l, θ)
g) Write the Lagrangian equation
h) Deduce the equations of motion from Euler-Lagrange equations