Question: Certain springs are characterized by decreasing stiffness with increasing deformation according to the relation F = k1x ?? k2x3 , where F is the force

Certain springs are characterized by decreasing stiffness with increasing deformation according to the relation F = k1x ?? k2x3 , where F is the force exerted by the spring, 1 k and 2 k are positive constants, and x is theeflection of the spring measured from its undeformed position. Determine

(a) The potential energy Ve as a function of x,

(b) The maximum velocity of a particle of mass m attached to the spring and released from rest with x = x0 . Neglect friction.

F = k+kx F = kx-kx

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