(a) What does the quadrupole formula (P) = = = (Qij Q³ ³) compute? Reason the answer. (b) A point mass m undergoes a harmonic motion along the z-axis with frequency w and amplitude L, x(t) = y(t) = 0, z(t) = L cos(wt). Show that the only non-vanishing component of the quadrupole moment tensor is = Im L² cos² (wt). (c) Use the quadrupole formula to compute the power radiated by the emission of gravitational waves. (Hint: recall that (cos(t)) = (sin(t)) = 0 and (cos² (t)) = (sin² (t)) = ½½ for a given frequency 2.)
(a) What does the quadrupole formula (P) = = = (Qij Q³ ³) compute? Reason the answer. (b) A point mass m undergoes a harmonic motion along the z-axis with frequency w and amplitude L, x(t) = y(t) = 0, z(t) = L cos(wt). Show that the only non-vanishing component of the quadrupole moment tensor is = Im L² cos² (wt). (c) Use the quadrupole formula to compute the power radiated by the emission of gravitational waves. (Hint: recall that (cos(t)) = (sin(t)) = 0 and (cos² (t)) = (sin² (t)) = ½½ for a given frequency 2.)
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Transcribed Image Text:(a) What does the quadrupole formula
(P) = = = (Qij Q³ ³)
compute? Reason the answer.
(b) A point mass m undergoes a harmonic motion along the z-axis with frequency w
and amplitude L,
x(t) = y(t) = 0, z(t) = L cos(wt).
Show that the only non-vanishing component of the quadrupole moment tensor is
=
Im L² cos² (wt).
(c) Use the quadrupole formula to compute the power radiated by the emission of
gravitational waves. (Hint: recall that (cos(t)) = (sin(t)) = 0 and
(cos² (t)) = (sin² (t)) = ½½ for a given frequency 2.)
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