Physics, 25.06.2020 07:01 pleasehelpmeonthis

An object suspended from a spring vibrates with simple harmonic motion. Part A At an instant when the displacement of the object is equal to one-fourth the amplitude, what fraction of the total energy of the system is kinetic

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Answer from: teacherpreacher

Complete Question

An object suspended from a spring vibrates with simple harmonic motion.

a. At an instant when the displacement of the object is equal to one-half the amplitude, what fraction of the total energy of the system is kinetic?

b. At an instant when the displacement of the object is equal to one-half the amplitude, what fraction of the total energy of the system is potential?

The fraction of the total energy of the system is kinetic energy $\frac{KE}{T} = \frac{3}{4}$

The fraction of the total energy of the system is potential energy $\frac{PE}{T} = \frac{1}{4}$

Explanation:

From the question we are told that

The displacement of the system is $e = \frac{a}{2}$

where a is the amplitude

Let denote the potential energy as PE which is mathematically represented as

$PE = \frac{1}{2} * k* x^2$

=> $PE = \frac{1}{2} * k* [\frac{a}{2} ]^2$

$PE = k* [\frac{a^2}{8} ]$

Let denote the total energy as T which is mathematically represented as

$T = \frac{1}{2} * k * a^2$

Let denote the kinetic energy as KE which is mathematically represented as

KE = T -PE

=> $KE =k [ \frac{a^2}{2} - \frac{a^2}{8} ]$

=> $KE =k [ \frac{3}{8} a^2 ]$

Now the fraction of the total energy that is kinetic energy is

$\frac{KE}{T} = \frac{ \frac{3ka^2}{8} }{\frac{ka^2}{2} }$

$\frac{KE}{T} = \frac{3}{4}$

Now the fraction of the total energy that is potential energy is

$\frac{PE}{T} = \frac{\frac{k a^2}{8} }{\frac{k a^2}{2} }$

$\frac{PE}{T} = \frac{1}{4}$

Answer from: Quest

Efficiency is an action of doing something. for example when you take a test. good efficiency means you did well but bad effeciency or no effiency means you did bad.

Answer from: Quest

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this. hope that you like the video and that it explains more in detail to you.

that is the link.

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