please explain clearly 1- Suppose you have a system that describes a prosthetic
ID: 1884864 • Letter: P
Question
please explain clearly
1- Suppose you have a system that describes a prosthetic leg behavior as shown in figure 1. and system input parameters are Mass (m), mechanical resistance b, and a spring constant k.; input signals Gravity(g) , and x0 , y0 , dx0/dt, and dy0/dt as initial positions and velocities.
if you set the following parameters
{m,b,k} = {100, 100,1000}
{x0, dx0/dt, y0, dy0/dt} to {0.3, 0, 0, 0}.
g = 0
and you plot x and y on the same plot to obtain tbe following graph
Provide a thorough, qualitative and quantitative explanation of what is happening in this scenario.
2- suppose you repeat the experiment but now the prosthetic leg is on Mars, i.e. set g = 3.7 N/kg, and you obtained the following plot
provide a detailed explanation of what happened?
1.1 m 0.9 m 0.7 m 0.5 m 0.3 m 0.1 mExplanation / Answer
Explaining the graph obtained in part a)
Line x defines the movement of the prosthetic limb in x-direction while y gives the movement in the y-direction. thus the dx/dt or the slope of the blue line is zero i.e. no motion in the x-direction.
We know that the prosthetic limb works like a spring. thus when the body applies a force on the leg, the leg holds some elastic energy. this is converted to gravitational potential energy and kinetic energy when it relaxes. hence there is a change in the y coordinate of the leg, therefore dy/dt increases. the small curve near the origin indicates that there is a decrease in height of the prostate leg when the force is applied.
For example, consider a spring(any spring, even the one in pens!). Apply a force on the spring by pushing the spring downward. The height of the spring decreases, elastic energy is stored. but due to newtons law, the spring comes up, the height of the spring increases.
So far the gravity is maintained to be zero, thus the effect of gravity is neglected.
Explanation for part b)
The presence of gravity does not change the spring constant (k). But it changes the equilibrium offset or the mean position of the spring. that's why there is the change or perturbation in the graph. The reason X line starts at 0.3 is due to the initial condition which is given as 0.3.
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