A differential equation question involving an axle undergoing SHM [Check my solutions]?
(a). Let θ is the rod’s angle from the vertical (measured from equilibrium state). Σtorque_around_axle I α -k x L cos θ - ? m g L sin θ (1/3) m L? (d?θ/dt?) canceled of L and simplified, -k (L sin θ) (1 - 2 sin? ? θ) - ? m g sin θ (1/3) m L (d?θ/dt?) for θ very small, -k L θ (1 - 0) - ? m g θ (1/3) m L (d?θ/dt?) -k L θ - ? m g θ (1/3) m L (d?θ/dt?) -(k L + ? m g)θ (1/3) m L (d?θ/dt?) all sides divided by (1/3) m L d?θ/dt? + 3(k/m + ? g/L)θ 0 (b). Let ω? 3(k/m + ? g/L) d?θ/dt? + ω?θ 0 θ(t) A sin ωt + B cos ωt dθ/dt Aω cos ωt - Bω sin ωt initial conditions, dθ/dt 0 at t 0 ? Aω cos ω * 0 - Bω sin ω * 0 Aω 0 A 0 θ(t) Φ at t 0 ? B cos ω * 0 B Φ Φ is initial angle of simple harmonic motion. general solution of differential equation is, θ(t) Φ cos ωt where ω? 3(k/m + ? g/L) (c). ω? 3(k/m + ? g/L) (2π/T)? 3(k/m + ? g/L) T 2π/√(3(k/m + ? g/L))
That is soooo easy! First, the love of my life Jim would be the person I would take because I would die without him, second the three things I would take, water, lots of food and third, my own private jet with none other than John Travolta as my personal pilot!!! :)
I would resign myself to my impending death. Therefore I would bring lots of rum, LSD, and crack cocaine. The person I would bring with me would be Paris Hilton. There's no way she would be able to survive on a tropical island either and her death would spare the world from her moronic attempts to become a celebrity. Im assuming its a tropical island and that I might be able to be eaten by sharks, a quick out. If it was an island near the Artic Circle death would that much quicker.
Like whitesox reported, there comes a ingredient the place you basically can no longer get a closed form answer. The (3x^2)^(x^2) is exceptionally complicated to combine. yet the place did each and all and sundry of those people come from. you have no longer have been given any contacts.
3 things I would take 1) Life supply of Jim Beam 2) Fishing Rod 3) Rifle (with life supply of bullets) - for hunting whatever is there Person - Anna Faris (because she has a good sense of humour and is really hot)
