Reading Material: Handout1, Handout 2 and Section 2.11 from Textbook for Linearization.\ Let us consider a mass

m

suspended from a ceiling by a string of length

l

as in the plane pendulum under the influence of gravity,

g

. However, the mass is allowed to swing in all directions. Your tasks are as follows:\ a) Compute an expression for total energy and angular momentum of mass

m

about pivot point of the pendulum.\ b) Comment on if energy and angular momentum are conserved or not.\ c) Repeat steps

a

) and

b

) if string is replaced by a spring of spring constant,

k

and rest length

l

.\ d) Write equations of motion for spring pendulum by making use of Lagrange's equations of motion.

Reading Material: Handout1, Handout 2 and Section 2.11 from Textbook for Linearization. 1) Let us consider a mass m suspended from a ceiling by a string of length l as in the plane pendulum under the influence of gravity, g. However, the mass is allowed to swing in all directions. Your tasks are as follows: a) Compute an expression for total energy and angular momentum of mass m about pivot point of the pendulum. b) Comment on if energy and angular momentum are conserved or not. c) Repeat steps a ) and b ) if string is replaced by a spring of spring constant, k and rest length l. d) Write equations of motion for spring pendulum by making use of Lagrange's equations of motion. (a) Spherical Pendulum (b) Rotary Pendulum