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The situation is represented on the picture. For the first question , I tried to do it with the conservation of mechanical energy. So I have the following $E = E_{cin} + E_{pot},mg + E_{pot}$,spring . But then I have a hard time expressing these. In order to find the maximal speed of P, I have to consider the case were potential energy is minimal, but writing the expression depending on $\phi$ is confusing. The second picture is what I managed to do until now. My attempt to solve the exercise

Can you help me please?

Here is the translation of the exercise : A paralellogram is made up of 4 rigid and homogeneous rods. Each rod has a main moment of inertia related to its centre of mass and equal to 1/12 times its mass times its length squared. rods AB, DC: length l; mass M rods BC, AD: length d; mass m The connections at points A,B,C,D are joints that do not fix the angles between the rods, but these 4 points are constrained to remain in a vertical plane. Points A and D are fixed to the ceiling. The springs have a zero open length and a stiffness constant k. The position of the system is indicated by the angle phi. Friction is neglected.

a) The rod BC is released from the ceiling with zero speed. Calculate the maximum speed of point P during the movement.

b) Find the differential equation for $\phi(t)$ from a first integral of the movement.What is the pulsation of the small oscillations around the stable equilibrium position?

c) While the system is stationary in its stable equilibrium position, one of the two springs breaks. What is the condition on k for the rods to hit the ceiling? Calculate the new equilibrium position and study its stability.

  • $\begingroup$ It'd be nice if you could concisely translate the question in english $\endgroup$ – aneet kumar Nov 22 at 11:28
  • $\begingroup$ atleast provide the reference for the question $\endgroup$ – Anonymous Nov 22 at 11:54
  • $\begingroup$ I have problems to start, so it's question a) $\endgroup$ – chloe2107 Nov 22 at 13:00