Need help setting up basic dynamics problem

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The discussion revolves around solving a dynamics problem involving point A, which oscillates with an acceleration equation of a=2880-144x. The user is trying to determine the maximum velocity and the positions where the velocity is zero, given a specific initial velocity of 11 in/s at x=20.4 in. The suggested approach involves integrating the acceleration equation to find the velocity equation and identifying critical points, but the user may be misinterpreting the initial conditions, as the velocity at x=20.4 in is not at maximum. Clarification is sought on the correct setup and understanding of the problem.
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point a oscillates with accel of a=2880-144x. Magnitude of velocity is 11in/s when x=20.4in. Determine the max velocity of A & two positions at which velocity is zero.

Why am I getting this wrong :( It seems so easy

integrate a=2880-144x to get v, plug in 11in/s and 20.4in as the initial values, solve for the constant and you get the velocity equation. From the acceleration equation you know there is a critical value at x=20in, so plugging x=20 to the velocity equation should give you the max velocity, and the other part is just finding the zeroes of v=...is that the right setup?
 
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Your initial value (v=11in/s) is NOT QUITE at maximum-velocity
location, so if you did not include a phase angle or time-offset,
(ending up with 20.917...) that might be your error.

umm, how do you know you're getting it wrong?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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