Finding spring constant by comparing to another spring

AI Thread Summary
In the discussion, two objects of equal mass are oscillating on different springs, with spring 1 having a known spring constant of 186 N/m and three times the amplitude of spring 2. The maximum velocity is the same for both objects, leading to a relationship between their spring constants. The user initially calculates the spring constant for spring 2 but arrives at an incorrect value of 20.6 N/m due to mixing up the springs in their calculations. Other participants suggest the user re-evaluate their approach to correctly determine the spring constant of spring 2. The conversation emphasizes careful analysis of the relationships in simple harmonic motion to find accurate results.
rasputin66
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Objects of equal mass are oscillating up and down in simple harmonic motion on two different vertical springs. The spring constant of spring 1 is 186 N/m. The motion of the object on spring 1 has 3 times the amplitude as the motion of the object on spring 2. The magnitude of the maximum velocity is the same in each case. Find the spring constant of spring 2.

My work...

Aw=Aw
A(sqrt of k/m) = A(sqrt k/m)
(sqrt of 186) = 3 (sqrt of k)
(sqrt of 186)/3 = (sqrt of k)
[(sqrt of 186)/3] ^2 = k
I got 20.6 but this is wrong, Please help!
 
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You're on the right track. You just got the springs mixed up. Do it over more carefully.
 
OH MY GOD. What is wrong with me??

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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