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Let the mass of the body is 25 gm, the force constant k be 400 dynes/cm, and let the motion be started
by displacing the body 10 cm to the right of its equilibrium position and imparting to it a velocity toward
the right of 40 cm/s.
Compute (a) the period, T, (b) the frequency f, (c) the angular frequency ω, (d) the
total energy E, (e) the amplitude A, (f) the angle θo, (g) the maximum velocity vmax ,(h) the maximum
acceleration a(max) , (i) the coordinate equations, velocity, and acceleration, and (j) displacement, velocity, acceleration at a time 𝜋/8 sec after the start of the motion.
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I'm new to blender. I want to restore sharp edge and create vertex that is geometrically intersection of selected triangles. Is there fast way to do this?
selected triangles are orange
This isn't very easy to do without changing the volume of the mesh, but here's the best method I've found:
Select the whole mesh (Or just the bevelled faces you want to sharpen):
Select the "Shrink/fatten" tool from the toolbar:
Shrink the faces, until the vertices at the corners are overlapping.
IMPORTANT: if you want to preserve the volume of the object, make sure to make a note of the exact value that you shrank the mesh by (visible in the bottom left of the screen):
Press the M key and select Merge by distance (or go to Mesh > Merge > By distance), and increase the Merge distance parameter until all of the vertices double vertices have been merged:
Finally, use the shrink/fatten tool again to resize the mesh to its original volume. (If you want to be exact, use the negative version of the amount you shrunk it by to begin with):
Bonus tip, if you want to get rid of the annoying triangles on the faces, you can use the Tris to quads operator to remove them.
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When I draw a cubic bezier curve with 4 control points,
I choose regular bezier path,
draw a line, then drag 2 handles out.
But now, I need draw a quartic curve with 5 control points.
I don't know how to do it.
How can I add the 5th control points in to handles?
Am I right to consider handles as control points?
Thank you, friends~~
I think that you are looking for a BSpline path rather than a regular Bezier path. This is the 3rd mode available (see your 1st attached screenshot).
Regular Bezier will interpolate (go through) your control points. BSpline is the classic N-degree Bézier.
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I'm studying the reduction about some hard problems on the lattice. What's the meaning of "worst case to average case reduction" ? For example, the paper "Worst-case to Average-case Reductions based on Gaussian Measures" gives the reduction from the worst case INCGDD problem to average case SIS problem, what does it mean?
A problem has average-case time complexity C if there exists an algorithm that solves the problem in C time on average, if the inputs are chosen randomly according to some distribution. Formalizing this is tricky, see here.
A problem has a worse case to average case reduction if you can show the following: if an algorithm solving the problem with average-case complexity C exists then this algorithm can be applied to also solve the worst-case with the same complexity (modulo a polynomial factor).
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I want to find the common eigenvectors of two symmetric matrices with the same dimension in R
Assuming two matrices L1 and L2 I am looking for vector X such that
L1*X = (landa)L2*X
where landa is the eigen value
The term you are looking for is Generalized Eigenvalue Problem. This is a well researched linear algebra problem.
In terms of implementation, I suggest looking at a special Netlib section, where I think your matrices will satisfy Generalized Symmetric Definite Eigenproblems solver requirements.
Intel MKL provides the functionality directly available from C, Fortran, and, as far as I know, Python.
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I'm learning the formal language and the theory of computation,
and new in draw finite automata.
So I want to ask how to draw FA or NFA for:
b*(ab) * a*
The simplified automaton is this one:
Where 1 is the starting state and all states are accepting states. It needs to be completed with a "Trash" state where all missing transitions will go.
Here I just drew a simple understandable NFA To demonstrate the solution for the given question
Image 1