Maximum Speed of a Mass on a Spring

AI Thread Summary
The discussion focuses on proving that the maximum speed (Vmax) of a mass on a spring is expressed as 2(pi)fA, where f is frequency and A is amplitude. Participants suggest starting with the equation of motion for a mass-spring system, which is Fx = kx, where k is the spring constant. To find Vmax, one must apply calculus to determine the maximum value of the motion equation. The conversation highlights the challenges faced by individuals with limited math backgrounds in understanding these concepts. Ultimately, grasping the relationship between frequency, amplitude, and maximum speed is essential for mastering the physics of oscillating systems.
Fittler
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How can I prove that the maximum speed (Vmax) of a mass on a spring is given by 2(pi)fA?

Where:
f= frequency
A= amplitude
pi= pi (3.14)

How can I do this?
:rolleyes:
 
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Write the equation of motion for the mass attached to a spring. Now, do you remember from calculus how to find the maximum of that equation?
 
I am so not a math buff. I do not even have my grade 11U Math. I am wokring through my math this semester. hehe. So, I have, in this physics course, come inot some difficulties. You know? Is the equation of motion for a mass attached to a spring Fx = kx?
 
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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