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We will consider a vibrating hydrogen molecule which in equilibrium has hydro- gen nuclei at (0,0, –4/2) and (0,0, l/2). Let (0,0, z1 (t)) be the position of the nuclei with equilibrium position (0,0, –4/2) and let (0, 0, z2(t)) be the position of the nuclei with equilibrium position (0,0, €/2). The system of equations for 21 (t) and z2(t) are myži(t) = k(z2(t) - 21(t) – () muž2(t) = -k(z2(t) – 1 (t) – (). Let s(t) = 22(t) – z1 (t) – l. (a) Find the equation for s(t). (b) Find the general solution to the equation for s(t). (c) Find the frequency of the vibrations of H2 with the harmonic vibration model.

We will consider a vibrating hydrogen molecule which in equilibrium has hydro- gen nuclei at (0,0, –4/2) and (0,0, l/2). Let (0,0, z1 (t)) be the position of the nuclei with equilibrium position (0,0, –4/2) and let (0, 0, z2(t)) be the position of the nuclei with equilibrium position (0,0, €/2). The system of equations for 21 (t) and z2(t) are myži(t) = k(z2(t) - 21(t) – () muž2(t) = -k(z2(t) – 1 (t) – (). Let s(t) = 22(t) – z1 (t) – l. (a) Find the equation for s(t). (b) Find the general solution to the equation for s(t). (c) Find the frequency of the vibrations of H2 with the harmonic vibration model.

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Please solve the following Advanced Mathematical Physics problem.

We will consider a vibrating hydrogen molecule which in equilibrium has hydro- gen nuclei at (0,0, –4/2) and (0,0, l/2). Let (0,0, z1 (t)) be the position of the nuclei with equilibrium position (0,0, –4/2) and let (0, 0, z2(t)) be the position of the nuclei with equilibrium position (0,0, €/2). The system of equations for 21 (t) and z2(t) are myži(t) = k(z2(t) - 21(t) – () muž2(t) = -k(z2(t) – 1 (t) – (). Let s(t) = 22(t) – z1 (t) – l. (a) Find the equation for s(t). (b) Find the general solution to the equation for s(t). (c) Find the frequency of the vibrations of H2 with the harmonic vibration model.
Transcribed Image Text:We will consider a vibrating hydrogen molecule which in equilibrium has hydro- gen nuclei at (0,0, –4/2) and (0,0, l/2). Let (0,0, z1 (t)) be the position of the nuclei with equilibrium position (0,0, –4/2) and let (0, 0, z2(t)) be the position of the nuclei with equilibrium position (0,0, €/2). The system of equations for 21 (t) and z2(t) are myži(t) = k(z2(t) - 21(t) – () muž2(t) = -k(z2(t) – 1 (t) – (). Let s(t) = 22(t) – z1 (t) – l. (a) Find the equation for s(t). (b) Find the general solution to the equation for s(t). (c) Find the frequency of the vibrations of H2 with the harmonic vibration model.
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