Oscillators A and B shown in the figure have the same amplitude and the same total energy. Their effective spring constants are k/4 and the series combination of k and k′, respectively. Find k′.

Question

G1 Physics · Accepted Answer

Equal amplitude and equal energy require equal effective spring constants. Oscillator A has kₑ=k/4. For B, k and k′ are in series: kₑ=kk′/(k+k′). Setting kk′/(k+k′)=k/4 gives 4k′=k+k′, so k′=k/3. Correct answer: A.