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 th

Question

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 ln 2 = 0 . 693 )

TestHub · Accepted Answer

The amplitude of damped oscillation with time $t$ and damping constant $b$ is given by,

$A = A_{0} e^{- b t / 2 m}$

$\Rightarrow \ln (\frac{A_{0}}{A}) = \frac{b t}{2 m}$

$\Rightarrow \ln 2 = \frac{b}{2 m} \times 120$ ; here $t = 2 \min = 120 s$

$\Rightarrow \frac{0.693 \times 2 \times 1}{120} = b$

$\Rightarrow b = 1.16 \times 10^{- 2} kg s^{- 1}$ .

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