Simple Nature - Light and Matter

h/Dependence of the amplitude and phase angle on the driving frequency, for an undamped oscillator. The amplitudes were calculat ...

right direction to add energy to the swing. At a driving frequency very different from the resonant frequency, we might get luck ...

force will simply displace the oscillator to one side, reaching an equilibrium that is offset from the usual one. The force and ...

k/The definition of ∆ω, the full width at half maximum. i/Example 45: a viola without a mute (left), and with a mute (right). Th ...

j/Dependence of the amplitude and phase angle on the driving frequency. The undamped case isQ =∞, and the other curves represent ...

l/The collapsed section of the Nimitz Freeway Collapse of the Nimitz Freeway example 47 Figure l shows a section of the Nimitz F ...

m/An x-versus-t graph of the steady-state motion of a swing being pushed at twice its resonant frequency by an impulsive force. ...

end up canceling out, however: Q= ωo ∆ω = 2 πfo 2 π∆f = fo f ≈ 10 In other words, once the musician stops blowing, the horn will ...

is also a solution of the driven equation. Here, as before,ωf is the frequency of the free oscillations (ωf ≈ωofor smallQ),ωis t ...

ticularly important for our purposes, but for completeness I’ll note, as you can easily verify, that the general solution to the ...

a/The car can change its x and y motions by one square every turn. 3.4 Motion in three dimensions 3.4.1 The Cartesian perspectiv ...

c/Bullets are dropped and shot at the same time. We call these thex,y, andzcomponents of the velocity and the momentum. There is ...

d/Two surfaces that could be used to extract energy from a stream of water. e/An asteroid absorbs visi- ble light from the sun, ...

direction as the motion, which will do positive work, increasing the asteroid’s energy and boosting it into an orbit with a grea ...

3.4.2 Rotational invariance The Cartesian approach requires that we choosex,y, and z axes. How do we choose them correctly? The ...

g/Two balls roll down a cone and onto a plane. Pythagorean theorem equals 1 √ ∆x^2 +∆y^2 +∆z^2 . Rotating a line segment doesn’t ...

3.4.3 Vectors Remember the title of this book? It would have been possible to obtain the result of example 55 by applying the Py ...

h/Example 56. of the three components, ∆px= 0 ∆py= 0 ∆pz= 0, or as a single vector equation,^16 ∆p= 0. The following table summa ...

i/Example 57. j/The geometric interpreta- tion of a vector’s components. be eliminated by dividing each equation bym, and we fin ...

k/Two vectors, 1, to which we apply the same operation in two different frames of reference, 2 and 3. A useless vector operation ...