 #1
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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