Question

(0.49,2.58) (2.60,1.37) (3.65,-1.00) 1.55,-1.88) -3 Engineers often describe damped harmonic motion with the formula x(t) - R e-sn sin(odt) because both ζ and ad can be measured in a straightforward way There is no phase shift ф because we have chosen an initial time t-0, to be a zero of x(t) If you measure the times and displacements, (ti,xi) and (t2,X2), at two consecutive peaks, then, T-t2 ti is called the quasi-period, and is the damped natural frequency or quasi-frequency 0I 2 Δ-In(-) is called the logarithmic decrement and 2 is called the damping ratio ~ V Δ2 + 4π2 s the (undamped) natural frequency Use the measured values of (ti,xi) and (t2,x2) from the graph above to find: @d 2.9 Now write the differential equation that x(t) satisfies in the form Finally, use the original formula and your measured values of (t1,X1) to estimate R and the initial conditions x(0) 0 x'(0)=

Answer 1

The step by step solution to the above problem is provided in the attached image file

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