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A particle of mass 3m is suspended from the ceiling by a spring of force constant k. A second particle of mass 2m is suspended from the first particle by a second identical spring. The rest lengths of both springs are lo. The particles can only move vertically. Gravity acts as usual in the vertical direction. i) ii) iii) iv) 3m 2m ееееееее k How many degrees of freedom does the system have? Choose appropriate generalised coordinates and write down the Lagrangian of the system in terms of them. Write down the Euler-Lagrange equations (the explicit equations, performing the derivatives of the Lagrangian). Find the equilibrium position of the particles. Is it stable?

A particle of mass 3m is suspended from the ceiling by a spring of force constant k. A second particle of mass 2m is suspended from the first particle by a second identical spring. The rest lengths of both springs are lo. The particles can only move vertically. Gravity acts as usual in the vertical direction. i) ii) iii) iv) 3m 2m ееееееее k How many degrees of freedom does the system have? Choose appropriate generalised coordinates and write down the Lagrangian of the system in terms of them. Write down the Euler-Lagrange equations (the explicit equations, performing the derivatives of the Lagrangian). Find the equilibrium position of the particles. Is it stable?

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A particle of mass 3m is suspended from the ceiling by a spring of force constant k. A second particle of mass 2m is suspended from the first particle by a second identical spring. The rest lengths of both springs are lo. The particles can only move vertically. Gravity acts as usual in the vertical direction. i) ii) iii) iv) ееееееее 3m 2m How many degrees of freedom does the system have? Choose appropriate generalised coordinates and write down the Lagrangian of the system in terms of them. Write down the Euler-Lagrange equations (the explicit equations, performing the derivatives of the Lagrangian). Find the equilibrium position of the particles. Is it stable?
Transcribed Image Text:A particle of mass 3m is suspended from the ceiling by a spring of force constant k. A second particle of mass 2m is suspended from the first particle by a second identical spring. The rest lengths of both springs are lo. The particles can only move vertically. Gravity acts as usual in the vertical direction. i) ii) iii) iv) ееееееее 3m 2m How many degrees of freedom does the system have? Choose appropriate generalised coordinates and write down the Lagrangian of the system in terms of them. Write down the Euler-Lagrange equations (the explicit equations, performing the derivatives of the Lagrangian). Find the equilibrium position of the particles. Is it stable?
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