Recent content by mkerikss

  1. M

    Power over current source and resistor in series

    Problem description: The problem is Kotitehtävä 7 in the attachement. The idea is to calculate the output power (both P and Q) of the current source. Attempt: I know the current through the current source (obviously) and want to calculate the voltage over it to get the power. I have...
  2. M

    Water molecules, surface tension and evaporation

    The relevant equations I can think of are: Q=Qvap*V (heat used for vaporization of V) W=S*A (work done to the water when increasing A) But these equations come straight from Qvap and S, (or they can be figured out) so that's why I didn't include them in my original post, but anyway, here...
  3. M

    Water molecules, surface tension and evaporation

    Homework Statement In this problem, the surface tension S represents the work done to the water when increasing the water's surface area. The vaporization temperature Qvap represents the energy needed per volume unit to vaporize water at 100 degrees Celsius. We imagine that water molecules...
  4. M

    What is the derivative of x(t,a) with respect to a when t=1 and a=0?

    1. I asked myself the same question. My guess it that x is a 1-variable function, and x(t,a) is used because a is supposed to be a variable in the second part of the problem, even if it's not originally a variable of the function x. So they're sort of trying to make things clearer by using...
  5. M

    What is the derivative of x(t,a) with respect to a when t=1 and a=0?

    Same as my previous post :tongue2: I brought this up so it wouldn't get lost in the depths of the forum!
  6. M

    Numerical methods for systems of differential equations

    Anyone? I'm preparing for a test tomorrow and would appreciate your help :smile:
  7. M

    The enaquality of the norm of the matrix e^(tA)

    Homework Statement Find the largest possible \alpha and the smallest possible \mu, so that for every t>0 e\alphat\leq IIetAII \leqe\mut when A=( 0 1) ----------(-1 -1) Homework Equations The inequality above always holds true when \alpha=\alpha(A) and \mu=\mu(A) The Attempt at...
  8. M

    Is there more than one possibility for eigenvectors of a single eigenvalue

    Ok, I noticed that now, if i multiply the first one with -i I get the second one and vice versa. Thank you :smile:
  9. M

    Numerical methods for systems of differential equations

    Homework Statement Consider the implicit (not actually sure wether that's the correct english word, my material is in Finnish and I'm Swedish-speaking :smile:) method xj+1=xj+h/2(f(tj,xj)+f(tj+h,xj+1)) a)Write an appropriate Runge-Kutta scheme b) What is the methods rank when we use the...
  10. M

    What is the derivative of x(t,a) with respect to a when t=1 and a=0?

    Homework Statement We consider the solution to the differential equation x'(t)=-x(t)+atx(t)2, x(0)=e as a function of the variable a. Define d/da x(t,a) t=1, a=0 Homework Equations The Attempt at a Solution I suppose the differentiation won't be too hard, but my problem is I just...
  11. M

    Is there more than one possibility for eigenvectors of a single eigenvalue

    I guess this is best explained with an example. The matrix (0 -1) has the eigenvalues ------------------------------------------------------------------ (1 0) i and -i. For -i we obtain ix1-x2=0 and x1+ix2=0. I got a corresponding eigen vector (1 i), but when I controlled this result with...
  12. M

    Change in an expression that I don't understand

    Homework Statement In the answer to a homework I didn't understnad why these are the same: d\vec{v}/dt*\vec{v}=d/dt(1/2\vec{v}*\vec{v}) Can someone explain? Homework Equations The Attempt at a Solution
  13. M

    Harmonic oscillator problem

    Homework Statement A particle with with the mass of m is attached to a spring (with no mass, spring constant k, length l) which is attached to a wall. The particle is moving with no friction along the x-axis. a) Write the particles motion equation, and find the general solution to the motion...
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