Question

answer this question as soon as possible...
I will mark uhh as branliest but no useless answers... ​

Answer 1

Answer:

velocity=Aw cos wt-Bw sin wt

acceleration=  -Aw^2 sin wt- BW^2 coswt= -w^2(A sinwt+B coswt)=  -   w^2*displacement

Explanation:

Answer 2

▶ Solution :

Given :

▪ A position → time equation of body is provided as

$\underline{\boxed{\bf{\pink{y=A\sin{\omega t}+B\cos{\omega t}}}}}$

▪ ω is constant.

To Find :

▪ Velocity and acceleration equation of body.

Concept :

$\star\bf\:v=\dfrac{dy}{dt}\\ \\ \star\bf\:a=\dfrac{dv}{dt}=\dfrac{d^2y}{dt^2}$

Calculation :

$\rightarrow\sf\:y=A\sin{\omega t}+B\cos{\omega t}\\ \\ \rightarrow\sf\:v=\dfrac{dy}{dt}=\dfrac{d(A\sin{\omega t}+B\cos{\omega t})}{dt}\\ \\ \rightarrow\sf\:v=A\omega\cos\omega t+B\omega(-\sin\omega t)\\ \\ \rightarrow\boxed{\bf{\green{v=A\omega\cos\omega t-B\omega\sin\omega t}}}\\ \\ \rightarrow\sf\:a=\dfrac{dv}{dt}=\dfrac{d(A\omega\cos\omega t-B\omega\sin\omega t)}{dt}\\ \\ \rightarrow\sf\:a=A{\omega}^2(-\sin\omega t)-B{\omega}^2\cos\omega t\\ \\ \rightarrow\boxed{\bf{\purple{a=-A{\omega}^2\sin\omega t-B{\omega}^2\cos\omega t}}}$