Question 102: 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 $$	imes$$ 102 kg s$$-$$1

Answer

3.3 $$	imes$$ 102 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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