Physics · University
Underdamped envelope after a time · formula reference
This is the amplitude envelope, not instantaneous signed displacement. The oscillator is specified as underdamped.
Formula
This is the amplitude envelope, not instantaneous signed displacement. The oscillator is specified as underdamped.
A(t) = A₀ exp[−bt/(2m)]
Worked example
An underdamped oscillator obeys m x″+b x′+kx=0 with m=7 kg, b=0.2 kg/s and initial envelope 39 cm. Find its envelope after 4 s. Round the final result to 4 decimal places if needed. Answer in cm.
The decay constant is b/(2m) = 0.2/(14) s⁻¹. Multiply the initial envelope by exp[−bt/(2m)].
36.8339 cm
Prerequisites and checking
Algebra, calculus and the stated physical model. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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