Solving Equation of Motion for A and \Phi

AI Thread Summary
The discussion revolves around solving the equation A sin(wt + Φ) = 0 to find the values of A and Φ. The user is unsure how to proceed, having been advised to use magnitude for A and another method for Φ. They have derived the angular frequency w but are struggling to find A and Φ using the original equation and its derivatives. The user seeks clarification on whether additional information is needed to solve the problem completely. Overall, the thread highlights the challenges faced in applying trigonometric identities and derivatives to solve for the unknowns in the equation of motion.
krnhseya
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Homework Statement



A sin (wt + \Phi) = 0
Find A and \Phi

Homework Equations



Asin(wt)cos\Phi + Acos(wt)sin\Phi = 0

The Attempt at a Solution



I was told to use magnitude to figure out A and something else to find \Phi in variable.
I absolutely have no idea what to do...
I found a part of solution, which got me w and I am expected to solve for A and \Phi with that given equation.

I tried to use original equation by plugging in t = 0 for A sin (wt + \Phi) and first and second derivative from original equation.

I think once I get those A and \Phi, I "might" be able to solve entire problem.

Thank you.
 
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is there missing info or ?
 
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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