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3 years ago

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(a) When the displacement in SHM is one-sixth the amplitude xm, what fraction of the total energy is kinetic energy? (b) What fr

action is potential energy? (c) At what displacement, in terms of the amplitude, is the energy of the system half kinetic energy and half potential energy? (Use any variable or symbol stated above as necessary.)

1 answer:

andreev551 [17]3 years ago

3 0

Answer:

Explanation:

$KE = \frac{1}{2}\times K\times (A^2-X^2)$

at $X = \frac{1}{6}A\\\\
KE = \frac{1}{2}\times K\times ( A^2 - A^{\frac{2}{36})\\\\
fraction = \frac{35}{36} = 0.9722
$

b) PE fraction = 1/36 = 0.02777

c) 1/2*KX^2 = 1/2*K*(A^2-X^2)

=> X = A/sqrt(2)

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<h3>What is simple harmonic motion?</h3>

Simple harmonic motion, in physics, repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side.

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This is only possible when cos θ = -1

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Using the value of spring constant, we can find the maximum potential energy.

$P.E =\frac{1}{2} k x^2\\P.E =\frac{1}{2} X 1.234 X 3.5^2 \\P.E = 7.56 J$

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The maximum mechanical energy is equal to the sum of maximum potential energy and the maximum kinetic energy.

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