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  • A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude of 12 cm. After 2 minutes the amplitude decreases to 6 cm. Determine the value of the damping constant for this motion. (take In 2 = 0.693)   <s

A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude of 12 cm. After 2 minutes the amplitude decreases to 6 cm. Determine the value of the damping constant for this motion. (take In 2 = 0.693)
 
Option: 1 5.7 \times 10^{-3}\; kg\; s^{-1}
Option: 2 1.16 \times 10^{-2}\; kg\; s^{-1}
Option: 3 3.3 \times 10^{2}\; kg\; s^{-1}  
Option: 4 0.69\times 10^{2}\; kg\; s^{-1}

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\begin{array}{l} \mathrm{A}=\mathrm{A}_{0} \mathrm{e}^{-\gamma t} \\ \\ \mathrm{In} 2=\frac{\mathrm{b}}{2 \mathrm{~m}} \times 120 \\ \\ \frac{0.693 \times 2 \times 1}{120}=\mathrm{b} \\ \\ 1.16 \times 10^{-2} \mathrm{~kg} / \mathrm{sec} \end{array}

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Deependra Verma

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