Reference no: EM131895641
Questions -
Q1. A particle of mass m slides on a smooth inclined plane under the uniform gravitational field. Using d'Alembert's principle, obtain the equation of motion.
![1516_figure.png](https://secure.expertsmind.com/CMSImages/1516_figure.png)
Q2. Consider the following spring-mass system on a smooth horizontal surface.
![1007_figure1.png](https://secure.expertsmind.com/CMSImages/1007_figure1.png)
If x1 and x2 are measured from their (M1, M2) equilibrium positions, write down the tagrangian of the system and obtain equations of motion.
Q3. The point of a support a simple pendulum of mass m and length l connected to a spring of spring constant k and constrained to move in y-direction.
![904_figure2.png](https://secure.expertsmind.com/CMSImages/904_figure2.png)
Using the covariant form of Newton's second law, d/dt (∂T/∂q·i) - ∂T/∂qi = Qi, where Qi = j=1∑n t→j(ext)· ∂r→/∂qi, obtain the equation of motion.
Q4. A mechanical system is described by the Lagrangian ⊥ = T - V with T = M/2[ω2 + α2θ· + 2αωθ·sin(θ-ωt)], V = mg(sinωt-αcosθ), where α, ω, m and g are constants.
a) Find an equivalent Lagrangian, Lew.
b) Obtain the energy function, h.
c) Is h a constant of motion. Explain.
d) Is h identical to the total energy (E) of the system. Explain.
e) Is E a constant of motion. Explain.