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johnq2k7
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Physics Advanced Oscillation problem, Help Needed!
Consider an atom of mass m bonded to the surface of a much larger immobile body by electromagnetic forces. The force binding the atom to the surface has the expression:
F= exp((a*cos(z))+(b*sin(z))) +d*tan(z)
where a,b, and d are constants and z is positive upwards. The equilibrium point is defined to be the origin, so z=0 there. Ignore an motion except in the vertical direction. THe whole assembly is subject to normal Earth gravity.
a.) For small oscillations, give an approx. expression for the binding force on the atom.
b.) What restriction are there on the values of a,b, and d so that the force on the atom actually is a restoring force and the atom can reach a stationary equilibrium?
c.) What is the angular frequency w_0 and frequency v_0 of oscillation of this undamped system?
d.) Would the oscillation frequency change if there were no gravity? Why?
e.) Subject to the considerations above, if the atom has a mass of 1 atomic mass unit, b= -1.658 x10^30 and d= -3.2361 x10^4 N, what is the frequency v_0 of he oscillation?
f.) Suppose that a photon with this frequency that is incident on this atom would absorbed. What wavelength does this correspond to? What part of the spectrum does it fall in?
I need a lot of help with these problems, help would be appreciated!
Consider an atom of mass m bonded to the surface of a much larger immobile body by electromagnetic forces. The force binding the atom to the surface has the expression:
F= exp((a*cos(z))+(b*sin(z))) +d*tan(z)
where a,b, and d are constants and z is positive upwards. The equilibrium point is defined to be the origin, so z=0 there. Ignore an motion except in the vertical direction. THe whole assembly is subject to normal Earth gravity.
a.) For small oscillations, give an approx. expression for the binding force on the atom.
b.) What restriction are there on the values of a,b, and d so that the force on the atom actually is a restoring force and the atom can reach a stationary equilibrium?
c.) What is the angular frequency w_0 and frequency v_0 of oscillation of this undamped system?
d.) Would the oscillation frequency change if there were no gravity? Why?
e.) Subject to the considerations above, if the atom has a mass of 1 atomic mass unit, b= -1.658 x10^30 and d= -3.2361 x10^4 N, what is the frequency v_0 of he oscillation?
f.) Suppose that a photon with this frequency that is incident on this atom would absorbed. What wavelength does this correspond to? What part of the spectrum does it fall in?
I need a lot of help with these problems, help would be appreciated!