c damping coefficient ranges from 2000 to 30000 Nsm m 1000k

c (damping coefficient) ranges from 2000 to 30000 N.s/m. m = 1000kg k = 81,000N/m y0 = 0 x0 = 1 E0 = 0.5*k*x0^2 + 0.5*m*v0^2 Using the equation as a function handle provided as function x = functionfile(t) % Free response function of a SDOF system global m c k global x0 v0 % m = mass c = damping coefficient % stiffness % x0 = initial displacement % y0 = initial velocity wn = squareroot (k/m); % natural frequency (\"omega_n\') zeta = c/2/ squareroot (k*m); % damping ration wd = wn* squareroot (1 - zeta^2); % damped natural frequency (\"omega_d\") if zeta = = 1; x = x0 + exp (-wn*t) + (v0 + wn*x0)*t. *exp(-wn*t); % critically damped case else x = exp(-zeta*wn*t)*(x0*cos(wd*t) + (v0+zeta*wn*x0)/wd*sin(wd*t)); end Find tr as the time instant when the mass is first dissipated to a specified level of the initial displacement, which is 5%. Find te as the time instant when the total mechanical energy of the system is dissipated to a specified level of initial energy, which is 5%. Graph tr and te as function of c. This must be done via MATLAB.

Solution

It decides that quadrant of the foundation node that the purpose ought to be in ( by checking the point\'s x and y against the horiontal center and vertical centers of the node\'s quad).
If there\'s a leaf node (let\'s decision it N) therein quadrant, it moves N\'s purpose into a toddler of N and adds the new purpose as a toddler of N also.
N is marked as a non-leaf as a result of it\'s kids.
By definition, a quadtree could be a tree during which every node has at the most four kids. Quadtree implementations — like D3\'s (source) — make sure that as points area unit further to the tree, nodes area unit rearranged such none of them have quite four kids.

Below area unit the graph of the quadtree and therefore the map of the points and rectangles it represents once more, side-by-side in order that you\'ll see however they relate to every different.

When a replacement purpose is inserted into a D3 quadtree:

It decides that quadrant of the foundation node that the purpose ought to be in ( by checking the point\'s x and y against the horiontal center and vertical centers of the node\'s quad).
If there\'s a leaf node (let\'s decision it N) therein quadrant, it moves N\'s purpose into a toddler of N and adds the new purpose as a toddler of N also.
N is marked as a non-leaf as a result of it\'s kids.
1. check out however the map correlates to the tree.
Click on Associate in Nursing parallelogram or purpose within the map read (below on the left). The tree read (below on the right) can pan to the corresponding node within the tree.

Zoom out and pan round the tree read to visualize the node in context.

2. check out however the tree correlates to the map.
Click on a tree node within the tree read. The map can highlight the realm or purpose that it represents.