A horizontal seismometer consists of a pendulum of length "l" constrained to rotate about a nearly vertical axis. The angle away from vertical for the axis is "a" (alpha) and the mass is "m"
a. Determine the Lagrangian for the system in terms of "theta", the angular displacement away from equilibrium about the axis.
b. Find the equation of motion.
c. In the limit of small "theta" find the natural frequency of oscillation
d. If "l" is 30cm, what value of "a" (alpha) will give a period of 10 seconds?
