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:
Explanation:
From the question we are told that:
Separation Distance 
Potential difference 
Generally the equation for Electric Field strength is mathematically given by
Answer:
ΔL =0. 000312 m
Explanation:
Given that
At room temperature ( T = 25 ∘C) ,L= 1 m
So the length at 13.0 ∘C above room temperature
L=1.000312 m
So the change in length
ΔL = 1.000312 - 1.0000 m
ΔL =0. 000312 m
Answer:
A dictatorship or tyranny.
Explanation:
