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`|@Sad20006@|`

\(37.\\x=A-4=1(cm)\\W_d=W-W_t\\=\dfrac{1}{2}kA^2-\dfrac{1}{2}kx^2=\dfrac{1}{2}.20.0,05^2-\dfrac{1}{2}.20.0,01^2=0,024(J)\\\longrightarrow A.\\38.\\A=10(cm)\\\omega=\dfrac{2\pi}{T}=2\pi(rad/s)\\W_d=W-W_t=\dfrac{1}{2}m\omega^2A^2-\dfrac{1}{2}m\omega^2x^2=\dfrac{1}{2}.0,1.(2\pi)^2(0,1^2-0,05^2)=0,0148=14,8.10^{-3}(J)\\\longrightarrow D.\\39.\\W=W_d+W_t=4W_t\\\Leftrightarrow \dfrac{1}{2}m\omega^2 A^2=2m\omega^2x^2\\\Leftrightarrow x^2=\dfrac{A^2}{4}\\\Leftrightarrow x=\pm\dfrac{A}{2}=\pm3(cm)\\\longrightarrow B.\\40.\\W=W_d+W_t=\dfrac{3}{2}W_t\\\Leftrightarrow \dfrac{1}{2}m\omega^2 A^2=\dfrac{3}{4}m\omega^2x^2\\\Leftrightarrow x^2=\dfrac{2A^2}{3}\\\Leftrightarrow x=\pm\dfrac{A\sqrt{6}}{3}=\pm\dfrac{4\sqrt{6}}{3}(cm)\\\omega=\sqrt{\dfrac{k}{m}}=10(rad/s)\\v=\pm\omega\sqrt{A^2-x^2}=\pm10\sqrt{4^2-\left(\dfrac{4\sqrt{6}}{3}\right)^2}=\pm\dfrac{40\sqrt{3}}{3}\approx 23(cm/s)\\\longrightarrow C.\\41.\\T=\dfrac{2\pi}{\omega}=\dfrac{2\pi}{4\pi}=\dfrac{1}{2}(s)\\T'=\dfrac{T}{2}=\dfrac{0,5}{2}=0,25(s)\\\longrightarrow D.\)