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Question Number 190257 by jlewis last updated on 30/Mar/23


Commented by jlewis last updated on 30/Mar/23

Commented by mahdipoor last updated on 31/Mar/23
$x=Asin(Bt+φ) ⇒ x^(..) +wx=−AB^2 sin(Bt+φ)+w^2 Asin(Bt+φ)=0 ⇒B=w ⇒ x=Asin(wt+φ) ⇒ { ((x(0)=0 ⇒ φ=0 or π)),((x^. (0)=v ⇒v=Awcosφ)) :} if: x=Asin(wt+φ) v>0 ⇒ φ=0 A=(v/w) v<0 ⇒ φ=π A=((−v)/w) v=0 ⇒ A=0$
$x = A s i n (B t + ϕ) \Rightarrow$ $\overset{. .}{x} + w x = - {A B}^{2} s i n (B t + ϕ) + w^{2} A s i n (B t + ϕ) = 0$ $\Rightarrow B = w \Rightarrow$ $x = A s i n (w t + ϕ) \Rightarrow {\begin{cases} x (0) = 0 \Rightarrow ϕ = 0 o r π \\ \dot{x} (0) = v \Rightarrow v = A w c o s ϕ \end{cases}$ $i f : x = A s i n (w t + ϕ)$ $v > 0 \Rightarrow ϕ = 0 A = \frac{v}{w}$ $v < 0 \Rightarrow ϕ = π A = \frac{- v}{w}$ $v = 0 \Rightarrow A = 0$
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