The expression for the motion of block in damped oscillation can be represented as:

Physics · JEE Main · NTA Exams — Oscillations and Waves

\(\mathrm{m} \frac{\mathrm{~d}^{2} \mathrm{x}}{\mathrm{dt}^{2}}+\mathrm{b} \frac{\mathrm{dx}}{\mathrm{dt}}+\mathrm{kx}=0\)
\(\mathrm{m} \frac{\mathrm{dx}}{\mathrm{dt}}+\mathrm{b} \frac{\mathrm{~d}^{2} \mathrm{x}}{\mathrm{dt}^{2}}+\mathrm{kx}=0\)
\(\mathrm{m} \frac{\mathrm{~d}^{2} \mathrm{x}}{\mathrm{dt}^{2}}+\mathrm{b} \frac{\mathrm{dx}}{\mathrm{dt}}-\mathrm{kx}=0\)
\(\mathrm{m} \frac{\mathrm{~d}^{2} \mathrm{x}}{\mathrm{dt}^{2}}-\mathrm{b} \frac{\mathrm{dx}}{\mathrm{dt}}-\mathrm{kx}=0\)

Answer

(A) m ~d ^ 2 x dt ^ 2 + b dx dt + kx =0

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