Energy and Time Period of a Pendulum in Simple Harmonic Motion

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The discussion focuses on the relationship between energy and the time period of a pendulum in simple harmonic motion without the small angle approximation. It emphasizes the need for mathematical analysis, suggesting that elliptic functions may arise in the solution. The original reference to Purcell is corrected to Berkeley Mechanics by Kittel for further reading. Participants agree that the problem is straightforward but requires deeper mathematical understanding. The conversation highlights the importance of accurate references in physics discussions.
Subhasish Mandal
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what is the relation between the energy &time period of a pendulam while not considering the small angle approximation,the given potential v(x)=Asinx
 
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this is a pretty straightforward question. u just hav to turn more mathematical cranks. u will find this worked out probably in Kleppner or in Purcell.
U get some sort of elliptic functions ( most probably)
 
sorry i mentoined the book wrong it should be Berkeley mechanics( Kittel) not purcell/ it was a slip of mind and i apologise
 
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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