# How to calculate the work done by the system

• rangareddy
In summary, your system oscillates around its mean position, and measures the force and displacement signals at input and output. The force and displacement signals are amplified and compared to one another to calculate the work done. Your system appears to be functioning efficiently, but you may need to adjust your input frequency to match the resonance frequency of the system.
rangareddy
HI I have some problem in calculation of the work dony by system.
the problem is i have one oscillatory mechanical system. For this system we r applying periodic force sinusoidally. for this system at entry and exit we are measuring the displacement signal and force signal. at resonance frequency the out put displacement and force signal is much higher than at input values. I am calculating the workd done at input and out put based on the formula W=|F|*|dx| based on this formula i am getting more work at output than input ,, is it mean that our system efficiency is more than 100%..
i am confusing where i am doing mistake.. can some one help me in this..
thanks

Hi, welcome to the forums. Your question is a little vague; may I ask that you supply a few more details? Specifically, can you explain precisely what kind of "oscillatory mechanical system" you are referring to? How does it work? What exact methods are you employing to measure the device's input and output force/work, and with what equipment? Don't worry about writing "too much" -- people here like a puzzle, but you need to supply more pieces before we have a chance of solving it!

You can think about the other energy sources in the system.I am not confirm, but this is one of the mistake that I do.

Hi Thanyou for your reply. I am giving the clear description of our system.

our system is consisting of more than twenty springs compressed and fixed in between two couplings. one end of this coupling is made fixed to the LDS vibrator and another end of this coupling is fixed to some mass(M). This LDS linear vibrator is going to give periodic force to this system and the system is going to oscilate to and fro around mean position like linear vibrator.we are measuring the force and displacement given to the system at input and force and displacement of the system at output using standard position sensor and force meter. During this process we are changing the frequency of the input force(vibrator) such that it should be equal to the resonance frequecny . after reaching this resonance frequency we observed as force and displament signals are out put and input.
main observation is out put signals both displacement and force is much higher than the input values. we are calculating the work at input and out put using the formula W=|F|*|dx| and summing up all these values for one period and calculating the power using W/T here T=period of the signal or T=1/f , f= frequency of the signal.
we observed that output power is allmost 20 times the input power and we are claiming as this system efficieny is more than 100% and amplifying the energy so it can be used as energy generator.
i am very confused here.. is this the way of calculation of work done is correct or wrong?
i am very eagerly want to know ur comments.

Thanks

## 1. What is work and how is it measured?

Work is a physical quantity that measures the amount of energy transferred to or from a system. It is measured in joules (J) and is calculated by multiplying the force applied to an object by the distance it travels in the direction of the force.

## 2. How do I calculate the work done by a constant force?

To calculate the work done by a constant force, you can use the formula W = F x d, where W is work, F is the force applied, and d is the distance traveled in the direction of the force. Make sure to use consistent units for force and distance, such as newtons (N) and meters (m).

## 3. Can the work done by a system be negative?

Yes, the work done by a system can be negative. This occurs when the force applied is in the opposite direction of the displacement of the object. For example, if you push a box to the left while it moves to the right, the work done by your force would be negative.

## 4. How do I calculate the work done by a variable force?

To calculate the work done by a variable force, you can use the formula W = ∫F(x) dx, where W is work, F(x) is the force at a specific position, and dx represents an infinitesimal change in position. This formula uses calculus and requires knowledge of the force function over the given distance.

## 5. Can you give an example of calculating work done by a system?

Sure! Let's say you lift a 10 kg box off the ground with a force of 50 newtons for a distance of 2 meters. The work done by the system would be W = F x d = 50 N x 2 m = 100 J. This means that 100 joules of energy were transferred to the box by your force.

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