01. i) Should the damping of a forced harmonic oscillator be large or small for a high and narrow resonance peak? ii) Figure 1 shows a tunnel in a uniform planet of mass M and radius R. At a distance r from the center, the gravitational attraction is due only to the sphere of radius r. Thus F = GmM(r) 7.2 mgr R where M(r) = Mr³/R³ and g = GM/R2. Show by Newton's 2nd law for the motion along the tunnel leads to the differential equation for SHM: x" (t) + 2/12x(t) = 0. Estimate the period of the oscillation for the earth. T
01. i) Should the damping of a forced harmonic oscillator be large or small for a high and narrow resonance peak? ii) Figure 1 shows a tunnel in a uniform planet of mass M and radius R. At a distance r from the center, the gravitational attraction is due only to the sphere of radius r. Thus F = GmM(r) 7.2 mgr R where M(r) = Mr³/R³ and g = GM/R2. Show by Newton's 2nd law for the motion along the tunnel leads to the differential equation for SHM: x" (t) + 2/12x(t) = 0. Estimate the period of the oscillation for the earth. T
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Transcribed Image Text:01.
i) Should the damping of a forced harmonic oscillator be large or small for
a high and narrow resonance peak ?
ii)
Figure 1 shows a tunnel in a uniform planet of mass M and radius
R. At a distance r from the center, the gravitational attraction is due only
to the sphere of radius r. Thus
F
GmM(r)
№.2
mgr
R
where M(r) = Mr³/R³ and g = GM/R². Show by Newton's 2nd law for
the motion along the tunnel leads to the differential equation for SHM:
x:"(t) + 2(t) = 0.
R
Estimate the period of the oscillation for the earth.
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