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An atom in a molecule oscillates about its equilibrium
Chapter 13, Problem 15P(choose chapter or problem)
Molecular Oscillations An atom in a molecule oscillates about its equilibrium position with a frequency of \(2.00 \times 10^{14} \mathrm{~Hz}\) and a maximum displacement of \(3.50 \mathrm{~nm}\). (a) Write an expression giving \(x\) as a function of time for this atom, assuming that \(x=A\) at \(t=0\). (b) If, instead, we assume that \(x=0\) at \(t=0\), would your expression for position versus time use a sine function or a cosine function? Explain.
Questions & Answers
QUESTION:
Molecular Oscillations An atom in a molecule oscillates about its equilibrium position with a frequency of \(2.00 \times 10^{14} \mathrm{~Hz}\) and a maximum displacement of \(3.50 \mathrm{~nm}\). (a) Write an expression giving \(x\) as a function of time for this atom, assuming that \(x=A\) at \(t=0\). (b) If, instead, we assume that \(x=0\) at \(t=0\), would your expression for position versus time use a sine function or a cosine function? Explain.
ANSWER:a.)
Step 1 of 2
We have to write an expression for displacement as a function of time for an atom oscillating about its equilibrium position with a frequency of
Hz.
The expression for displacement as a function of time is given by,
where,
Amplitude = 3.50 nm
angular speed in rad/s
Now,
Where,
frequency of oscillations
= Hz
Thus,
= rad/s
Hence,
Therefore, the expression for displacement as a function of time is
b.)