Question 78: Oscillations

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)

Accepted Answer

$A = {A_o}{e^{{{ - b} \over {2m}}t}}$
$ \Rightarrow $ $6 = 12{e^{{{ - b} \over {2 	imes 1}} 	imes 120}}$
$ \Rightarrow $ $6 = 12{e^{ - b 	imes 60}}$
$ \Rightarrow $ ${1 \over 2} = {e^{ - 60b}}$
$ \Rightarrow $ $\ln (2) = 60b$
$ \Rightarrow $ $b = {{\ln (2)} \over {60}} = 1.16 	imes {10^2}$ Kg/s

Answer

0.69 $	imes$ 10
2
kg s
$-$1

Answer

3.3 $	imes$ 10
2
kg s
$-$1

Answer

1.16 $	imes$ 10
$-$2
kg s
$-$1

Answer

5.7 $	imes$ 10
$-$3
kg s
$-$1

Oscillations

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)

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