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A problem set from a university physics course, phy 711, focusing on the wave equation for a uniform wire with given initial value information. Students are required to use maple or other software to find the analytic form of the function and plot the function and its derivative at two different time instances.
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October 10, 2007
PHY 711 – Problem Set # 14
Start reading Chapter 7 in Fetter and Walecka.
= c^2
∂^2 f ∂x^2
In this equation, c represents a known constant which depends on the tension and the mass per unit length of the wire. Also suppose that the following initial value information is known: f (x, t)ct=0 = 0. (2) ∂f (x, t) ∂t
⌋
t=
sinh(x) cosh^2 (x)
(a) Use Maple or other software to plot f (x, t)ct=0 and
∂f (x, t) ∂t
⌋
t=
(b) Find the analytic form of f (x, t) for some t > 0.
(c) Use Maple or other software to plot f (x, t) and
∂f (x, t) ∂t
for at least two values of t > 0.