Calculate the ratio of the kinetic energy to the potential energy of a simple ha

Question

Calculate the ratio of the kinetic energy to the potential energy of a simple harmonic oscillator when its displacement is 1/3 of its amplitude. (The answer is an integer.)

Approach: Choose a specific trigonometric form for the position function x(t). It doesn't matter which since the answer doesn't depend on the initial conditions. Let the amplitude be 'A' (which will cancel when you compute the ratio). Determine v(t) that corresponds to your choice of x(t). Apply the given displacement condition to determine what your choice of x(t) was equal to (you don't need to try and compute a time: the result holds for any simple harmonic oscillator). From this directly compute the desired ratio. The trig identity sin2(?)+cos2(?)=1, which as discussed in class is equivalent to the conservation of energy here, will definitely be helpful.

Explanation / Answer

P.E = 0.5*k*(a/3)2 = ka2/18

Total Energy = ka2/2

K.E = T.E - P.E

= 8ka2/18

ratio of kinetic and potencial energy is 8:1

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.