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Hello, First post hear so bear with me.

I have a mass in free fall with a viscous friction which can be derived from the dissipative potential Kv

L=T-V=[itex]\frac{1}{2}[/itex]m[itex]\dot{y}[/itex][itex]^{2}[/itex]-mgy-[itex]\frac{1}{2}[/itex]k[itex]\dot{y}[/itex][itex]^{2}[/itex]=[itex]\frac{1}{2}[/itex](m-k)[itex]\dot{y}[/itex][itex]^{2}[/itex]-mgy

When I do the Euler-Lagrange:

[itex]\ddot{y}[/itex]=-mg/(m-k)

However, from this equation I cant proove that maximum velocity.

Any help will be appreciated.

I have a mass in free fall with a viscous friction which can be derived from the dissipative potential Kv

^{2}/2. I must find the Lagrangian and proove that the maximum speed is v=mg/K. I have the following Lagrangian:L=T-V=[itex]\frac{1}{2}[/itex]m[itex]\dot{y}[/itex][itex]^{2}[/itex]-mgy-[itex]\frac{1}{2}[/itex]k[itex]\dot{y}[/itex][itex]^{2}[/itex]=[itex]\frac{1}{2}[/itex](m-k)[itex]\dot{y}[/itex][itex]^{2}[/itex]-mgy

When I do the Euler-Lagrange:

[itex]\ddot{y}[/itex]=-mg/(m-k)

However, from this equation I cant proove that maximum velocity.

Any help will be appreciated.

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