A particle moves along the x axis subject to a force toward the origin proportional to x (say −kx). Show that the particle executes simple harmonic motion (Example 3). Find the kinetic energy 1/2mv2 and the potential energy 1/2 kx2 as functions of t and show that the total energy is constant. Find the time averages of the potential energy and the kinetic energy and show that these averages are each equal to one-half the total energy (see average values, Chapter 7, Section 4).
A particle moves along the x axis subject to a force toward the origin proportional to x (say −kx). Show that the particle executes simple harmonic motion (Example 3). Find the kinetic energy 1/2mv2 and the potential energy 1/2 kx2 as functions of t and show that the total energy is constant. Find the time averages of the potential energy and the kinetic energy and show that these averages are each equal to one-half the total energy (see average values, Chapter 7, Section 4).
Related questions
Question
A particle moves along the x axis subject to a force toward the origin proportional to x (say −kx). Show that the particle executes
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
