The greenhouse-gas carbon dioxide molecule CO2strongly absorbs infrared radiation when its vibrationalnormal modes are excited by light at the normal-modefrequencies. CO₂ is a linear triatomic molecule, asshown in (Figure 1), with oxygen atoms of mass mobonded to a central carbon atom of mass mc. Youknow from chemistry that the atomic masses of carbonand oxygen are, respectively, 12 and 16. Assume thatthe bond is an ideal spring with spring constant k.There are two normal modes of this system for whichoscillations take place along the axis. (You can ignoreadditional bending modes.) In this problem, you will findthe normal modes and then use experimental data todetermine the bond spring constant.FigureO1mo1x₁2mc1 of 13mo1XzPart ALet x₁, x2, and 3 be the atoms' positions measured from their equilibrium positions. First, use Hooke's law to write the net forceon each atom. Pay close attention to signs! For each oxygen, the net force equals mod²x/dt². Carbon has a different mass, so itsnet force is mcd²x/dt². Define a² = k/mo and 3² = k/mc. Find an equation for the second derivative of ₁ coordinate.Express your answer in terms of some, all, or none of the variables ₁, 2, 3, and the constants a, ß.17 ΑΣΦd²x₁dt²SubmitPart Bd²x2dt²Request AnswerFind an equation for the second derivative of 2 coordinate.Express your answer in terms of some, all, or none of the variables ₁, 2, 3, and the constants a, B.=?——| ΑΣΦ?

Hooke's law is given as F=-kx Here F,k,x are restoring force, spring constant and extension in…

The greenhouse-gas carbon dioxide molecule CO2 strongly absorbs infrared radiation when its vibrational normal modes are excited by light at the normal-mode frequencies. CO₂ is a linear triatomic molecule, as shown in (Figure 1), with oxygen atoms of mass mo bonded to a central carbon atom of mass mc. You bonded to care know from chemistry that the atomic masses of carbon pective 12 and 16 and oxygen are, respectively, 12 and 16. Assume that the bond is an ideal spring with spring constant k There are two normal modes of this system for which oscillations take place along the axis. (You can ignore additional bending modes.) In this problem, you will find the normal modes and then use experimental data to determine the bond spring constant. Figure O mo C 2 mc. < 1 of 1 0 3 mo www. 1 X3 > Part A Let ₁, 2, and 3 be the atoms' positions measured from their equilibrium positions. First, use Hooke's law to write the net force on each atom. Pay close attention to signs! For each oxygen, the net force equals mod²x/dt². Carbon has a different mass, so it net force is mcd²x/dt². Define a² = k/mo and 32 = k/mc. Find an equation for the second derivative of ₁ coordinate. Express your answer in terms of some, all, or none of the variables ₁, 2, 3, and the constants a, B. 195] ΑΣΦ dt² Submit ▾ Part B Request Answer d²x₂ dt2 Find an equation for the second derivative of 2 coordinate. Express your answer in terms of some, all, or none of the variables ₁, 2, 3, and the constants a, B. ? VE] ΑΣΦ ?

The greenhouse-gas carbon dioxide molecule CO2 strongly absorbs infrared radiation when its vibrational normal modes are excited by light at the normal-mode frequencies. CO₂ is a linear triatomic molecule, as shown in (Figure 1), with oxygen atoms of mass mo bonded to a central carbon atom of mass mc. You bonded to care know from chemistry that the atomic masses of carbon pective 12 and 16 and oxygen are, respectively, 12 and 16. Assume that the bond is an ideal spring with spring constant k There are two normal modes of this system for which oscillations take place along the axis. (You can ignore additional bending modes.) In this problem, you will find the normal modes and then use experimental data to determine the bond spring constant. Figure O mo C 2 mc. < 1 of 1 0 3 mo www. 1 X3 > Part A Let ₁, 2, and 3 be the atoms' positions measured from their equilibrium positions. First, use Hooke's law to write the net force on each atom. Pay close attention to signs! For each oxygen, the net force equals mod²x/dt². Carbon has a different mass, so it net force is mcd²x/dt². Define a² = k/mo and 32 = k/mc. Find an equation for the second derivative of ₁ coordinate. Express your answer in terms of some, all, or none of the variables ₁, 2, 3, and the constants a, B. 195] ΑΣΦ dt² Submit ▾ Part B Request Answer d²x₂ dt2 Find an equation for the second derivative of 2 coordinate. Express your answer in terms of some, all, or none of the variables ₁, 2, 3, and the constants a, B. ? VE] ΑΣΦ ?