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1. Modelling A Stiff Base With A Mass Spring System

Hi all. I am working on a problem in which I want to model the collision of a moving object, with mass m1, with a stationary base. I have calculated the velocity of the moving object at the instant of collision. I want to model this collision using a mass spring system with damping. My...
2. Linearly Independent Sets and Bases

Homework Statement V is a subspace of Rn and S={v1,...,vk} is a set of linearly independent vector in V. I have to prove that any list of linearly independent vectors can be extended to a basis for V. Homework Equations None that I can think of. The Attempt at a Solution So to be...
3. Proof of logarithmic properties.

Ah I get it now! Thanks :)
4. Proof of logarithmic properties.

Thanks for your help. I worked out part 1, but I'm still unsure on part 2. For proving the law for a natural number I did: Let y=ln(a), for a>0, ey=a, and if we raise each side to the power n we get: (ey)n=an ln(ey*n)=ln(an) y*n = ln(an), but y = ln(a) n*ln(a) = ln(an) So I'm still...
5. Proof of logarithmic properties.

Homework Statement There are two log properties that I have to prove: 1) Explain why ln(b1/n)=(1/n)ln(b) for b>0, set b=an 2) Explain why ln(ar)=rln(a) for any r in Q and a>0, ie r is rational. Homework Equations ln(an)=nln(a) The Attempt at a Solution In a previous question...
6. Use Upper And Lower Sums To Evaluate An Integral

That makes perfect sense! Thanks a bunch :D
7. Use Upper And Lower Sums To Evaluate An Integral

Homework Statement The question is to use upper and lowers sums, Un and Ln, on a regular petition of the intervals to find the integral from 1 to 2 of f(x) = [[x]], where [[x]] is the greatest integer function. Homework Equations \Deltax = \frac{b-a}{n} The Attempt at a Solution \Deltax =...
8. Motion Around An Ellipse

That doesn't work. I have an example in my book with x=1.0m and hence y=sqrt(0.75). They give v=10.4m/s, however your method gives v=6.55m/s.
9. Motion Around An Ellipse

Homework Statement There is an elliptical path and pegs A and B are restricted to move around it. If the link moves with a constant speed of 10m/s, determine the magnitude of velocity when x=0.6m [PLAIN]http://users.adam.com.au/shortround/Prob.12-78.jpg [Broken] Homework Equations...
10. Physics Projectile Motion Question

Thanks rl.baht! I had just managed to work it out using the same method :)
11. Physics Projectile Motion Question

In my textbook they have an example where the initial velocity is 24m/s and they give the answer as \theta=24.8o below the horizontal and \theta=85.1o above the horizontal. Okay using v^2 = v_0^2 + 2 a \Delta x I found the final velocity in the y direction to be...
12. Physics Projectile Motion Question

I understand that the initial horizontal velocity is 28cos\theta and the vertical component is 28sin\theta. As iraten said I could then substitute it into v^2 = v_0^2 + 2 a \Delta x , but we do not know the final velocity when the water hits the wall. In the horizontal direction a=0...
13. Physics Projectile Motion Question

Homework Statement The question is: A fireman at point A wishes to put out a fire at B. Determine the two possible angles \theta1 and \theta2 at which this can be done. The water flows from the hose at vA=28m/s and the value for gravity is 9.81m/s2...