homework 1
薛定谔方程代写 Two identical masses are connected with 3 identical springs, as shown. Write F=ma for each of the masses. You should get a pair of
1. Solve the following diff eqs for the function y(x) in the interval 0 < x < L. In A what are the allowed values of the constant k? 薛定谔方程代写
2. Consider this triangular probability density function: 薛定谔方程代写
(a) What must be the value of A?
(b) Find the mean and variance of the random varible x described by this pdf.
- Two identical masses are connected with 3 identical springs, as shown. Write F=ma for each of the masses. You should get a pair of coupled differential equations
involving the displacements x1(t) and x2(t) and the accelerations x1’’(t) and x2’’(t). Substitute in sinusoidal solutions:
x1(t)=A1 coswt and x2(t)=A2 coswt The cosine functions will then drop out, giving two algebraic equations for the two amplitudes A1 and A2
Show that this set of equations has a non-trivial solution only if the frequency w has one of the two values: 薛定谔方程代写
What does the motion of the masses look like in each of these two cases?
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