Total energy of a mass hanging on a spring

[arhzz]

Homework Statement

An object with an mass of m = 1 kg hangs on a vertical spring (k = 100 N / m) and vibrates with an amplitude of 0.05 m.

a) What is the maximum potential energy of this oscillator and how large is the total energy?

Relevant Equations

Et = Ep +Ek

Hello!

So here what I did is first calculated the potential energy; $$ E_p = \frac{1}{2} * k * x^2 $$ E_p should be = 0,125 J Now i tried calculating the kinetic energy, I used this formula $$ E_k = \frac{mv^2}{2} $$ to get v I used this formula $$v = x *\sqrt{\frac{k}{m}} $$ v should be = 0,5 m/s. If we plug that back in the formula for kinetic energy get 0,125 J as well. Now the total energy should be the sum of these two which means $E_t = 0,25 J$ But this was graded wrong by my teacher,the right answer is 0,125 J. But I don't understand how? I'd assume we have no kinetic energy but since the it is vibrating (moving) kinetic energy should exist. What am I missing here?

Thanks!

 

[Hamiltonian]

$$v = x *\sqrt{\frac{k}{m}} $$

I think this is not correct.
for a a particle performing SHM $$v(x) = \omega(A^2 - x^2)^{1/2}$$
where $\omega = (k/m)^{1/2}$(the agular frequency) and $A$ is the maximum displacement of the body from its mean position.

 

[arhzz]

I think this is not correct.
for a a particle performing SHM $$v(x) = \omega(A^2 - x^2)^{1/2}$$
where $\omega = (k/m)^{1/2}$(the agular frequency) and $A$ is the maximum displacement of the body from its mean position.

Hmm okay that would actually make sence,that my calculation of Ek was wrong.Although I have never seen this formula before,I'll give it a shot. And could you please tell me what SHM means?

 

[DrClaude]

Hmm okay that would actually make sence,that my calculation of Ek was wrong.Although I have never seen this formula before,I'll give it a shot. And could you please tell me what SHM means?

SHM stands for Simple Harmonic Motion.

Check out fig. 15.3.2 at https://phys.libretexts.org/Bookshe...tions/15.03:_Energy_in_Simple_Harmonic_Motion

 

[arhzz]

SHM stands for Simple Harmonic Motion.

Check out fig. 15.3.2 at https://phys.libretexts.org/Bookshelves/University_Physics/Book:_University_Physics_(OpenStax)/Book:_University_Physics_I_-_Mechanics,_Sound,_Oscillations,_and_Waves_(OpenStax)/15:_Oscillations/15.03:_Energy_in_Simple_Harmonic_Motion

Excellent,I'll read through this and get back to you!

 

[willem2]

a) What is the maximum potential energy of this oscillator and how large is the total energy?
Relevant Equations:: Et = Ep +Ek

I'd assume we have no kinetic energy but since the it is vibrating (moving) kinetic energy should exist. What am I missing here?

If you want the use the maximum potential energy and the maximum kinetic energy to calculate the total energy, you should make sure the maxima are reached at the same time.

 

[arhzz]

Okay so to give a quick anwer,I have figure it out thanks to the link provided by DrClaude.After reading through this should be no problem to understanding this problem.https://phys.libretexts.org/Bookshe...tions/15.03:_Energy_in_Simple_Harmonic_Motion

The link once more.

Thank you for your help!

 

[rsk]

You have worked out the maximum ke and the maximum ke. However, you can't simply add them to find the total energy, because when the ke is max, the pe is minimum and vice versa.

Max v and Max ke at equlibrium position
Max pe at max dispacement, where v and hence ke are instantaneously zero.

 

[kuruman]

If you want the use the maximum potential energy and the maximum kinetic energy to calculate the total energy, you should make sure the maxima are reached at the same time.

You don't really mean this, do you? How can the maxima be reached at the same time?

 

[willem2]

You don't really mean this, do you? How can the maxima be reached at the same time?

I said, that the maxima had to occur at the same time IF you wanted to add the maximum potential and kinetic energy

 

[kuruman]

I said, that the maxima had to occur at the same time IF you wanted to add the maximum potential and kinetic energy

That's not what you said in post #6. In any case, the maxima never occur at the same time so why even bother mentioning the addition of the two maxima? I am trying to see what your point is.

 

[willem2]

That's not what you said in post #6. In any case, the maxima never occur at the same time so why even bother mentioning the addition of the two maxima? I am trying to see what your point is.

Yes, that is precisely what I said in post #6, and also what appears to have gone wrong in #1.

 

[kuruman]

OK, I see your point. Thanks.