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Energy of a particle attached to 3 springs

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I am having trouble with the type of question listed below and any help would be greatly appreciated. I have attached a diagram also.

A block P of mass m is attached to three springs whose other ends are attached to fixed points A, B and C. I have listed the stiffnesses of the three springs and their natural lengths below. The point B is a distance 5L below A, and the point C is a distance 1/2L above B.

Spring = AP, Stiffness = 2k, Natural length = L
Spring = BP, Stiffness = 8k, Natural length = 1/2L
Spring = CP, Stiffness = 6k, Natural length = 3/2L

What should the datum for gravitational potential energy of particle P be? Why choose this point?
What is the gravitational potential energy of particle P at a general point of its motion?
What is the kinetic energy of particle P at a general point of its motion?
What is the potential energy stored in each spring at a general point of its motion?
How would I write an equation representing the total mechanical energy for the system at a general point of its motion?

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Solution Summary

Equilibrium problems. Energy in springs. Elastic potential and kinetic energy. Conservation of energy. Hooke's Law.

Solution provided by:
Chris Busu, PhD (IP)
Education
  • BSc, University of Bucharest
  • MSc, Ovidius
  • MSc, Stony Brook
  • PhD (IP), Stony Brook
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