The angular frequency of a damped oscillator is ω=√[k/m-r²/(4m²)]. If r²/(mk)=8%, the approximate change in time period relative to the undamped oscillator is:
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Question

The angular frequency of a damped oscillator is ω=√[k/m−r²/(4m²)]. If r²/(mk)=8%, the approximate change in time period relative to the undamped oscillator is:

G1 Physics · Accepted Answer

Let ω₀²=k/m. Then ω²=ω₀²[1−r²/(4mk)]=0.98ω₀², so ω≈0.99ω₀ and T/T₀≈1.01. The time period increases by about 1%. Hence option C.