Applied Mathmatics


  

Consider the frictionless rod, i.e. β=0. The equation of agitation becomes

m (d^2 r)/(dt^2 )-mω^2 r=-mg sin⁡(ωt)

with g=9.81 m/s^2 and a uniform anfractuous press ω.

The rod is judiciously downright, and the judicious conditions for the study are r(0)=r_0 and r^′ (0)=v_0.

A)Analytically clear-up this judicious prize gist for r(t) B)Consider the judicious comcomposition to be nothing, i.e. r_0=0. Perceive the judicious swiftness, v_0, that results in a resolution, r(t), which displays uncompounded harmonic agitation, i.e. a reredisentanglement that does not nurture toward eternity. C)Explain why any judicious swiftness besides the one you institute in divorce B) causes the study to fly off the rod. D)Given r(t) displays uncompounded harmonic agitation, i.e. divorce B), perceive the incompleteness required extension of the rod, L, as a employment of the anfractuous press, ω. E)Suppose ω=2, graph the resolutions, r(t), for the judicious conditions absorbed here: r_0=0 and judicious velocities of v_0=2.40, 2.45, 2.50, and the judicious swiftness you institute in divorce B). Use 0≤t≤5