Asked by Anonymous
It looks very complicated and I do not know how to even start. Any help would be immensely appreciated.
A pendulum has a mass, m, suspended from a rod of length L. At the time t = 0, the pendulum is pulled through an angle θ0 > 0 to the right and given an initial velocity of vo. The angular displacement of the pendulum at time t is then given by
θ(t) = θocos(ωt) + (vo/ωL)sin(ωt)
where ω = sqrt(9.81/L). Show that this angular displacement can be expressed as
θ(t) = sqrt(θo^2w^2L^2 + vo^2/w^2L^2)sin(wt+φ)
where φ = arctan (wLθo/vo).
A pendulum has a mass, m, suspended from a rod of length L. At the time t = 0, the pendulum is pulled through an angle θ0 > 0 to the right and given an initial velocity of vo. The angular displacement of the pendulum at time t is then given by
θ(t) = θocos(ωt) + (vo/ωL)sin(ωt)
where ω = sqrt(9.81/L). Show that this angular displacement can be expressed as
θ(t) = sqrt(θo^2w^2L^2 + vo^2/w^2L^2)sin(wt+φ)
where φ = arctan (wLθo/vo).
Answers
Answered by
Steve
simple, but tedious. See
http://en.wikibooks.org/wiki/Trigonometry/Simplifying_a_sin%28x%29_%2B_b_cos%28x%29
http://en.wikibooks.org/wiki/Trigonometry/Simplifying_a_sin%28x%29_%2B_b_cos%28x%29
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