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10 points Question 3. Consider the harmonic oscillator =v, ů= -war. (a) Show that the orbits are given by ellipses of th
Posted: Thu May 12, 2022 12:44 pm
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- 10 Points Question 3 Consider The Harmonic Oscillator V U War A Show That The Orbits Are Given By Ellipses Of Th 1 (45.46 KiB) Viewed 28 times
10 points Question 3. Consider the harmonic oscillator =v, ů= -war. (a) Show that the orbits are given by ellipses of the form w222 +02 = C, where C > 0. (5 subpts) (Hint: One possible approach is to divide the equation by the u equation, seperate the variables (u's from x's), and then integrate the resulting seperable equation.) (b) Show that this condition is equivalent to the conservation of energy. (5 subpts) (Hint: The harmonic oscillator with mass m and spring constant k stores a fixed constant amount of energy, which is the sum of the kinetic and potential energy. One possible approach to this question is to show that this sum is of the form of the ellipse given in Part (a).)