# Mechanical energy of a mass-spring system

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In summary, the mechanical energy of a mass-spring system with speed v at position x is E = .5mv^2 + .5kx^2.
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Hey,
Stuck on finding the mechanical energy of a mass-spring system, my question is as follows > A mass-spring system oscillates with an amplitude of .026 m. The spring constant is 290 N/m and the mass is 0.50 kg, it asks for the mechanical energy in (J). and the maximum acceleration of the mass-spring system which is 15.08 m/s (verified, webassign rules).

Mechanical energy is confusing to me, I am pretty determined it might be potential(PE)enery + kinetic energy(KE), but ofcourse the formula for KE involves velocity. I only have the acceleration so I feel I have gone astray along the way.

Basically I am having trouble finding where to start and then I'm wondering how to get the answer in Joules.

Thanks.

The mechanical energy of a mass-spring system with speed v at position x is $$E = .5mv^2 + .5kx^2$$ .

Pick a point in the oscillation and apply this equation. (Hint: there's a special point in its motion which simplifies this problem greatly).

Skomatth said:
The mechanical energy of a mass-spring system with speed v at position x is $$E = .5mv^2 + .5kx^2$$ .

Pick a point in the oscillation and apply this equation. (Hint: there's a special point in its motion which simplifies this problem greatly).

Thanks for the reply. I assume when you say pick a point you mean pick a point to plug in for the variable V. The amplitude is .026m

So far I have this

E=.25v^2 + 0.09802

Would V be 1/2 of the maximum acceleration?

When the mass it as its maximum displacement what is its velocity? You should know this without having to use a formula. If you don't, review the chapter.

Last edited:
Skomatth said:
When the mass it as its maximum displacement what is its velocity? You should know this without having to use a formula. If you don't, review the chapter.

The chapter has been read very carefully by me twice. We haven't really covered mass at its maximum displacement, or maybe we have and called it something else.

I think by maximum displacement you mean the amplitude which is ofcourse .026m. Maximum accel. is 15.08 m/s . I realize the answer is probably smack in front of me but with only one submission left on web assign I remain wary. I still am a bit confused at how to find the velocity with mass, amplitude, max. accel, and 290N/M.

Wow I am stupid!
KE= 1/2 290 N/m * (.026)^2

Thanks!

## 1. What is a mass-spring system?

A mass-spring system is a physical system composed of a mass attached to a spring that can compress or stretch. The system exhibits oscillatory motion, where the mass moves back and forth around a equilibrium point due to the force of the spring.

## 2. How does a mass-spring system store and release energy?

The spring in a mass-spring system stores potential energy when it is compressed or stretched. This potential energy is then converted into kinetic energy as the mass moves back and forth, releasing the energy stored in the spring.

## 3. What factors affect the amount of mechanical energy in a mass-spring system?

The amount of mechanical energy in a mass-spring system is affected by the mass of the object, the spring constant, and the amplitude of oscillation. A higher mass or spring constant will result in greater energy, while a larger amplitude will result in more energy being released.

## 4. How is the mechanical energy of a mass-spring system calculated?

The mechanical energy of a mass-spring system is calculated as the sum of the potential energy (due to the compressed or stretched spring) and the kinetic energy (due to the motion of the mass). This can be represented by the equation E = 1/2 kx2 + 1/2 mv2, where k is the spring constant, x is the displacement of the spring, m is the mass, and v is the velocity of the mass.

## 5. Why is the mechanical energy of a mass-spring system considered a conservative quantity?

The mechanical energy of a mass-spring system is considered conservative because it remains constant as long as there are no external forces acting on the system. This means that the energy is conserved and can be transferred between potential and kinetic forms without any losses.

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