Recent content by Henryk

This is a classic coupled oscillators problem. The solution involves finding the eigenvalues of the matrix, that is the values of ##\omega## which will make the determinant of the matrix equal to zero. That part is already done for you and you are given one value of normal frequency equal to...

There is no such thing as not "really" true in mathematics. Maybe the general theory states that the physical space is not actually flat, but that doesn't mean we can't construct a true flat space in mathematics.

Yes, A rotating magnet creates an AC magnetic field. That induces currents within the conductive surface which, by Lentz law, oppose the changes in the magnetic field, ergo, create a repelling force. This principle has been applied to Maglev trains.

It depend on how big the sail is, really.

your first equation is wrong. You are adding squared velocity term to kinetic energy term! ##v^2 + \frac 1 2 mv^2##

well, the famous 21 cm hydrogen line is associated with the transition between 1s to 1s, the difference comes from parallel to antiparallel aligning of the elecron spon with the proton spin.

Your answer 9.1 is (approximately) correct. It means it will fly over 9 steps and land on the 10th.

I can see that your energy reference point is: the spring is fully extended and the weight is placed on top of that. The energy the will have three components: potential energy due to gravity equal -mgd, plus spring potential energy, equal to ##\frac 1 2 kd^2## and the kinetic energy ##\frac 1/2...

Yes, they are Same mass, same charge, same spin, same magnetic moment, all of their properties are the same.

oops, sorry, I have a symbol missing in Ampere's law, it should be ##\oint \vec H \cdot \vec l = I##, i.e. dot product, not cross product and I is the total current enclosed by the loop with the direction given by the right hand rule. Now, you notice that you can move vertical vectors left or...

You also have to think about the pressure of the collected hydrogen. All gasses are easily compressible.

Use Ampere's law ##\oint \vec H d \vec l = I## twice. Use a rectangular path (which have to be in the plane perpendicular to the current direction). The first one would have to include pieces of all three current planes; this would give you the field on both sides of the stack of planes. The...

I had some relays failtures. It turned out that solder joints were cracked. Check all the joints, specially the high currrent ones unde a good magnifying glass.

I was told that the power factor is given as ##PF = \frac P {V*I}##. I don't understand where did you get the coefficient 1.732 (or is it 0.732??). Now, the true power is given by (in case where both, current and voltage are sinusoidal) ##P = V * I * cos(\phi)##, in other words, power factor is...

I don't think your equations are correct. First of all, since the convertor operates in continuous current mode, the average (over a switching period) inductor current equals average current throug the diode when it conducts. Let us define I(t) - inductor current averaged over a switching...