3. The following potential energy function is called the GST potential: U(x) = -bx? + cx+ with b and a as positive constants. a. Sketch this potential as a function of x. b. Assuming the particle in this potential will move only along the f direction, find the force felt by this particle. c. Find the location of any equilibrium points for this potential and determine their stability.
3. The following potential energy function is called the GST potential: U(x) = -bx? + cx+ with b and a as positive constants. a. Sketch this potential as a function of x. b. Assuming the particle in this potential will move only along the f direction, find the force felt by this particle. c. Find the location of any equilibrium points for this potential and determine their stability.
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Transcribed Image Text:3. The following potential energy function is called the GST potential:
U(x) = -bx? + cx+
with b and a as positive constants.
a. Sketch this potential as a function of x.
b. Assuming the particle in this potential will move only along the î direction, find the force felt by this
particle.
c. Find the location of any equilibrium points for this potential and determine their stability.
d. If the particle starts at x =
, find the turning point in its motion (if there is one).
e. Determine the maximum kinetic energy of the particle.
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