(1) Find the parameters k, ω, and (9%)

題組內容

1. There is a sinusoidal transverse wave travelling along a string in the positive direction of an x axis. The displacement y of the string particle at x=0 is given in Fig. 1 as a function of time t. The scale of the vertical axis is set by yz=0.04m. The wave equation is to be in the form y(x,t) = ym sin(kx ± ωt + φ).

2. Fig.2 shows a circuit section of four air-filled capacitors that is connected to a larger circuit. The graph below the section shows the electric potential V(x) as a function of position x along the lower part of the section, through capacitor 4. Similarly, the graph above the section shows the electric potential V(x) as a function of position x along the upper part of the section, through capacitors 1, 2, and 3. Capacitor 3 has a capacitance of 0.8 μF. What are the capacitances of (a) capacitor 1 (4%) and (b) capacitor 2 ? (4%)

題組內容

(1) Find the parameters \( k \), \( \omega \), and \( \varphi \) (9%)

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