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4

The term "gradient" implies a change in some quantity versus a change in second quantity, usually over a distance. It's very much like a slope. For example, the gradient of a roof line on a house is given as rise/run like 15 cm/m or 5 inches/foot. The gradient of potential is the electric field magnitude, with SI units of volts/meter. A magnetic field is ...

3

A 'gradient' measures how quickly something changes with respect to something else. In this case, it's how much the magnetic field strength changes per unit length.

2

You have reasoned correctly that one should measure from the point the pendulum pivots about. You missed to see however, that if you are in the the resonance scenario, the 'common support swing' is swinging to and fro too, and the line the string of the pendulum in resonance / the driving one forms lies in the same plane as the common swing. I.e. the pendula ...

0

A dipole is fed by a frequency varying voltage [or current] source at the center between the two halves. In theory, you send a sinusoidal signal down the transmission line which will see the dipole two dipole leads as an impedance $Z_{ant}$. For a half-wave dipole, $Z_{ant} \approx 72 + j42.5$ $\Omega$. The classical textbook analysis of the radiation from ...

2

I first thought, that you have a $\frac 0 0$ or $\frac\infty\infty$ in both cases, but it's wrong. In (a) you get $R = l/\omega$ and in (b) too you can just naively insert $\infty$ for $\omega$ and get $R = \frac{(l\omega)^2}{\omega^4}$, and thus an $\frac 1{\infty^2}$ as the result. But actually I think the physical meaning is more interesting and I'm not ...

3

It's probably the temperature of glass itself. Speed of sound in solids depends on the elastic moduli (the choice of the modulus depends on the polarization of sound - in this case, it's mostly transverse motion, as you are observing glass oscillation). The change of the density of the hot air may also contribute. Possible contributions and why they can be ...

1

Glass contracts when heated. This means the individual molecules compact as they meet the heat catalyst. This is one reason for the resonance difference. But also: If you take two separate glasses and fill them at different levels of room temperature water you will find they have different resonant frequencies as well. So in your heated liquid experiment ...

1

Your transfer function appears to be representing the relative displacement between $M_1$ and $M_2$ as a result of an input excitation, $W$, presumably a force. This simplified linear model is often used to express the dynamics of an automotive suspension system where $M_1$ is the mass of the vehicle and $M_2$ is the mass of the suspension mechanism and ...

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