The starting angle θθ of a pendulum does not affect its period for θ<<1θ<<1. At higher angles, however, the period TT increases with increasing θθ.
The relation between TT and θθ can be derived by solving the equation of motion of the simple pendulum (from F=ma)
−gsinθ=lθ¨−gainθ=lθ¨
For small angles, θ≪1,θ≪1, and hence sinθ≈θsinθ≈θ. Hence,
θ¨=−glθθ¨=−glθ
This second-order differential equation can be solved to get θ=θ0cos(ωt),ω=gl−−√θ=θ0cos(ωt),ω=gl. The period is thus T=2πω=2πlg−−√T=2πω=2πlg, which is independent of the starting angle θ0θ0.
For large angles, however, the above derivation is invalid. Without going into the derivation, the general expression of the period is T=2πlg−−√(1+θ2016+...)T=2πlg(1+θ0216+...). At large angles, the θ2016θ0216 term starts to grow big and cause
Answer:
The decision designer is a step-wise process
Explanation:
A typical decision tree will be like this:
Are there any forces?
YES - then calculate the resultant forces NO - Then no calculations are needed
IF YES - Are the forces balanced? NO - Then no calculations
IF YES - Then calculations can be done.
Resolve the forces to find the resultant of the forces in the question.
This version of Einstein’s equation is often used directly to find what value? E = ∆mc2
Answer: This version of Einstein’s equation is often used directly to find the mass that is lost in a fusion reaction. Therefore the correct answer to this question is answer choice C).
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Biosphere is the answer, hope i helped :))
Answer:
Explanation:
so a mechanical wave transfers energy through a medium but unlike other waves that move through very long distances
the distance of the mechanical wave is different
