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Consider the arrangement shown below, where a mass m is attached to two light identical springs that are in turn attached to two rigid walls a distance 2l apart. The springs have force constant k and equilibrium length lo. Neglect the force of gravity and assume that the system is frictionless. m ll 2l (a) Suppose l = lo. Show that for small transverse displacements (Jx| « l6) the equation of motion is * + ya = 0, (1) %3D where y = k/ml, is a positive constant. (b) Suppose l > lo. Show that the equation of motion (1) changes to * + ax + yr° = 0, (2) where a = 2k(l – lo)/ml and y= k/ml² are positive constants.

Consider the arrangement shown below, where a mass m is attached to two light identical springs that are in turn attached to two rigid walls a distance 2l apart. The springs have force constant k and equilibrium length lo. Neglect the force of gravity and assume that the system is frictionless. m ll 2l (a) Suppose l = lo. Show that for small transverse displacements (Jx| « l6) the equation of motion is * + ya = 0, (1) %3D where y = k/ml, is a positive constant. (b) Suppose l > lo. Show that the equation of motion (1) changes to * + ax + yr° = 0, (2) where a = 2k(l – lo)/ml and y= k/ml² are positive constants.

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Consider the arrangement shown below, where a mass m is attached to two light identical springs that are in turn attached to two rigid walls a distance 2l apart. The springs have force constant k and equilibrium length lo. Neglect the force of gravity and assume that the system is frictionless. k ll k ll m -2l (a) Suppose l = lo. Show that for small transverse displacements (r| « lo) the equation of motion is ä + ya3 = = 0, (1) where y = k/ml, is a positive constant. (b) Suppose l > lo. Show that the equation of motion (1) changes to * + ax + yx = 0, (2) where a = 2k(l – lo)/ml and y= k/ml² are positive constants.
Transcribed Image Text:Consider the arrangement shown below, where a mass m is attached to two light identical springs that are in turn attached to two rigid walls a distance 2l apart. The springs have force constant k and equilibrium length lo. Neglect the force of gravity and assume that the system is frictionless. k ll k ll m -2l (a) Suppose l = lo. Show that for small transverse displacements (r| « lo) the equation of motion is ä + ya3 = = 0, (1) where y = k/ml, is a positive constant. (b) Suppose l > lo. Show that the equation of motion (1) changes to * + ax + yx = 0, (2) where a = 2k(l – lo)/ml and y= k/ml² are positive constants.
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