Question

For lightly damped harmonic oscillators the displacement is given by x(t) = (A^(-bt/2m))*cos(ωt + φ) with period T = 2π / (sqrt((k/m)-(b^2/(4m^2)))). A) Show that this equation of motion obeys the force equation for a damped oscillator: F = −kx − bv. B) Shock absorbers in a pickup truck are designed to have a significant amount of damping. The effective spring constant of the four shock absorbers in a 1600 kg truck have an effective spring constant of 157,000 N/m. Suppose a truck hits a large speed bump, causing the carriage to bounce. If the initial oscillation amplitude is 40 cm and this decreases to 2.2 mm in 4 oscillations, what is the effective damping constant of the shocks?

Answer 1

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