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fer Mnaj

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- Homework Statement
- Given this expression : ##a(t)=−\omega^2(C_1\cos \theta+C_2\sin\theta)##

And with two initial conditions ##x(0)=x_0## and ##v(0)=v_0##

How to get velocity and position?

Furthermore, Can we get the values of ##C_1## and ##C_2##, what are these?

- Relevant Equations
- centripetal aceleration is the most likely ##a(t)=−\omega^2(\cos\theta+\sin\theta)##

this expression : ##a(t) = −ω^2 (C_1 \cos θ + C_2 \sin θ)##

I´ve never seen it before, where is it from?

It kinda looks like centripetal acceleration, but what exactly are ##C_1## and ##C_2##?

Can we calculate its velocity and position?

If I´ve got two initial conditions ##x(0)=x_0## and ##v(0)=v_0##I thought we could get velocity and position

with:

##\omega=\theta/t## IS constant

##dv/dt= −ω^2 (C_1 \cos θ + C_2 \sin θ)##

##\int dv=\int−ω^2 (C_1 \cos \omega t + C_2 \sin \omega t)dt##

##-\int1/w^2 dv=C_1\int \cos (\omega t) dt+ C_2\int\sin (\omega t) dt## is it correct?

Is it solvable?

I´ve never seen it before, where is it from?

It kinda looks like centripetal acceleration, but what exactly are ##C_1## and ##C_2##?

Can we calculate its velocity and position?

If I´ve got two initial conditions ##x(0)=x_0## and ##v(0)=v_0##I thought we could get velocity and position

with:

##\omega=\theta/t## IS constant

##dv/dt= −ω^2 (C_1 \cos θ + C_2 \sin θ)##

##\int dv=\int−ω^2 (C_1 \cos \omega t + C_2 \sin \omega t)dt##

##-\int1/w^2 dv=C_1\int \cos (\omega t) dt+ C_2\int\sin (\omega t) dt## is it correct?

Is it solvable?

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