A simple harmonic oscillator of amplitude A has a total energy E . (a) Determine

Question

A simple harmonic oscillator of amplitude A has a total energy E.

(a) Determine the kinetic energy when the position is one-third the amplitude. (Use any variable or symbol stated above as necessary.)
K =

(b) Determine the potential energy when the position is one-third the amplitude. (Use any variable or symbol stated above as necessary.)
U =

(c) For what values of the position does the kinetic energy equal one-half the potential energy? (Use any variable or symbol stated above as necessary.)
x = ±

(d) Are there any values of the position where the kinetic energy is greater than the maximum potential energy?

YesNo    

Explain.

Explanation / Answer

Max energy = 1/2 KA^2 where K is the spring constant, A is the amplitude

a) at x = A/3

KE + 1/2 K ( A/3)^2 = 1/ 2 KA^2

KE = 1/2KA^2 ( 1- 1/9) = 1/2 KA^2 ( 8/9) ---8/9 of full energy

b)PE = 1/9 ( 1/2KA^2) or 1/9 of fill energy

c) 1/2 Kx^2 = 1/2 ( 1/2 KA^2)

x^2 = A^2/2

x= +- A/ sqroot (2)

d) Yes, for all values lying between + A/ sqroot 2 and - A/ sqroot 2 ,KE will greater than PE

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