Say that a spring can move in x, y, and z. How should I find the...
Say that a spring can move in x, y, and z. How should I find the spring constant k if the displacements of x, y, and z are known (through a graph that features position vs time)? Does k present itself as k_x, k_y, and k_z? Then does that mean |k|=sqrt{k_x^2+k_y^2+k_z^2}?
Homework Answers
Spring constant is not a vector quantity it is a scalar quantity. So k does not have any effect of direction it will be same in all direction. You can see it by this formula
here k is constant but it is multiplied in all direction.
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the...
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
8.) (12 pts.) Find the Flux of the Vector Field F(x, y, z) = (z)i +...
8.) (12 pts.) Find the Flux of the Vector Field F(x, y, z) = (z)i + (x)} + (y)k through Surface S, which is that portion of the plane 2++2 = 3 is the 1st octant, and r is the unit normal vector pointing away from the origin.
1. A 1 kg mass is attached to a spring of spring constant k = 4kg/82, The spring-mass system is a...
Differntial Equations Forced Spring Motion
1. A 1 kg mass is attached to a spring of spring constant k = 4kg/82, The spring-mass system is attached to a machine that supplies an external driving force of f(t) = 4 cos(wt). The systern is started from equilibrium i.e. 2(0) = 0 and z'(0) = 0. There is no damping. (a) Find the position x(t) of the mass as a function of time (b) write your answer in the form r(t)-1 sin(6t)...
Find the spring constant for the given data in the static method by plotting Displacement (along...
Find the spring constant for the given data in the static method by plotting Displacement (along y-axis) vs. Added Mass (along x-axis). Recall: the slope of the trend line corresponds to g/k. Copy and paste your graph here. (2 pts) Added Mass (kg) Displacement (m) 0.05 0.11 0.10 0.20 0.15 0.31 0.20 0.43 0.25 0.54 0.30 0.62 0.35 0.78 0.40 0.90 Again, find the spring constant for the same spring using the dynamic method, i.e. by plotting T2 (along y-axis)...
Find the flux of the field F(x,y,z)=z² i +xj - 3z k outward through the surface...
Find the flux of the field F(x,y,z)=z² i +xj - 3z k outward through the surface cut from the parabolic cylinder z=1-yby the planes x = 0, x=2, and z=0. The flux is (Simplify your answer.)
04: Use a surface integral to find the outward flux of F = x i + y j + z k through the surface of the sphere za. 04: Use a surface integral to find the outward flux of F = x i + y j + z k th...
04: Use a surface integral to find the outward flux of F = x i + y j + z k through the surface of the sphere za.
04: Use a surface integral to find the outward flux of F = x i + y j + z k through the surface of the sphere za.
Please answer these two questions, thx. Astronaut X Astronaut Y 70 60 50 Z 40 30...
Please answer these two questions, thx.
Astronaut X Astronaut Y 70 60 50 Z 40 30 20 10 Figure 1 Astronaut X Astronaut Y 0.1 0.2 0.3 0.4 Spring Length (m) Figure 2 36. The graph above shows the force exerted by a spring as a function of the length of the spring. A block on a frictionless table is pushed against the spring that is fastened to a wall. The spring is compressed until its length is 20 cm....
Consider the given vector field. F(x, y, z) = (9 / sqrt(x2 + y2 + z2))...
Consider the given vector field. F(x, y, z) = (9 / sqrt(x2 + y2 + z2)) (x i + y j + z k) Find the curl of the vector field. Then find Divergence
Find the work done by force F=3(sqrt)z i−3x j+(sqrt)y k, from (0,0,0) to (1,1,1) over each of the... Find the work done by force F=3(sqrt)z i−3x j+(sqrt)y k, from (0,0,0) to (1,1,1) over each of the f...
Find the work done by force F=3(sqrt)z i−3x j+(sqrt)y k, from (0,0,0) to (1,1,1) over each of the... Find the work done by force F=3(sqrt)z i−3x j+(sqrt)y k, from (0,0,0) to (1,1,1) over each of the following paths. C1 =ti +tj +tk, C2 =ti + t2j + t4k, and C3∪C4 c1=7/6 c2=-1/5 what is c3uc4?
Activity 2. Finding the spring constant of a spring: DYNAMIC METHOD A spring of length L...
Activity 2. Finding the spring constant of a spring: DYNAMIC METHOD A spring of length L is connected to a support. A small mass m is connected to the spring pulling on this mass, the spring is stretched down a distance A from its equilibrium position. When the mass is let go, it starts oscillating up and down. The position of the mass changes as shown in the graph below. a) What type of motion does the graph describe? b)...
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
8.) (12 pts.) Find the Flux of the Vector Field F(x, y, z) = (z)i + (x)} + (y)k through Surface S, which is that portion of the plane 2++2 = 3 is the 1st octant, and r is the unit normal vector pointing away from the origin.
Differntial Equations Forced Spring Motion
1. A 1 kg mass is attached to a spring of spring constant k = 4kg/82, The spring-mass system is attached to a machine that supplies an external driving force of f(t) = 4 cos(wt). The systern is started from equilibrium i.e. 2(0) = 0 and z'(0) = 0. There is no damping. (a) Find the position x(t) of the mass as a function of time (b) write your answer in the form r(t)-1 sin(6t)...
Find the flux of the field F(x,y,z)=z² i +xj - 3z k outward through the surface cut from the parabolic cylinder z=1-yby the planes x = 0, x=2, and z=0. The flux is (Simplify your answer.)
04: Use a surface integral to find the outward flux of F = x i + y j + z k through the surface of the sphere za.
04: Use a surface integral to find the outward flux of F = x i + y j + z k through the surface of the sphere za.
Please answer these two questions, thx.
Astronaut X Astronaut Y 70 60 50 Z 40 30 20 10 Figure 1 Astronaut X Astronaut Y 0.1 0.2 0.3 0.4 Spring Length (m) Figure 2 36. The graph above shows the force exerted by a spring as a function of the length of the spring. A block on a frictionless table is pushed against the spring that is fastened to a wall. The spring is compressed until its length is 20 cm....
Activity 2. Finding the spring constant of a spring: DYNAMIC METHOD A spring of length L is connected to a support. A small mass m is connected to the spring pulling on this mass, the spring is stretched down a distance A from its equilibrium position. When the mass is let go, it starts oscillating up and down. The position of the mass changes as shown in the graph below. a) What type of motion does the graph describe? b)...
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