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Question: specifically need help with 33...

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O Problem 3 (Logan 1.2 Problem 5 p. 42) Consider the nonlinear spring-mass system IVP mr(t)--k(z(t))3-ar(t) t20 x(0)0 where z is the displacement, -ar is a linear damping term, and -kr3 is a nonlinear restoring force. Initially, displacement is zero and mass m is given an impulse I 3.1 [5 points] Determine the dimensions of the constants I, a, and k 3.2 [10 points] Recast the problem into dimensionless form by selecting dimensionless variables τ-t/te, χ- scale tc is yet to be determined az/I, where the time 3.3 [10 points] In the special case that the mass is very small [compared to something else with dimensions of mass], choose an appropriate time scale te and find the correct dimensionless model. (A small dimensionless parameter should occur on the terms involving the mass in the original model).
Specifically need help with 3.3.

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