Pendulum-displacement-amplitude of vibration

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The discussion centers on calculating the amplitude of a swing's vibration, where a child swings through a total of 42 degrees. It is clarified that amplitude represents the maximum displacement from the equilibrium position, which in this case is half of the total swing angle, resulting in an amplitude of 21 degrees. The small angle approximation is mentioned, indicating that this calculation is valid for angles below 45 degrees. Participants confirm that the correct answer is indeed 21 degrees, reflecting a successful understanding of the concept. The conversation emphasizes the relationship between total displacement and amplitude in oscillatory motion.
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Homework Statement


A child on a playground swings through a total of 42 degrees. If the displacement is equal on each side of the equilibrium position, what is the amplitude of this vibration?
(Disregard frictional forces acting on the swing)

The Attempt at a Solution


I know amplitude is the maximum displacement, but I am not sure how to get the answer with the degrees.
Would it just be 42 degrees?
 
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Just came to my mind: usually amplitude of a sinusoidal function is taken from equilibrium position to maximum displacement, so it would be 21 degrees. If the small angle approximation holds (usually you can assume it holds for amplitudes below 45 degrees) the angular position of the boy could be described by:

angle = 21 cos (2*pi/T * t) [degrees]

where T is the oscillation period.

kcmccraw said:

Homework Statement


A child on a playground swings through a total of 42 degrees. If the displacement is equal on each side of the equilibrium position, what is the amplitude of this vibration?
(Disregard frictional forces acting on the swing)




The Attempt at a Solution


I know amplitude is the maximum displacement, but I am not sure how to get the answer with the degrees.
Would it just be 42 degrees?
 
yeaaaa it's 21! i got it right on the test a few days ago i had to guess though :( :D thanks.
 
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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