A spring supports a mass of 5 g which performs damped oscillations. It is found to have successive maxima of 2.1 cm and 1.3 cm. If the damping coefficient b is 10 g s − 1 , find the time interval betw

Question

A spring supports a mass of 5 g which performs damped oscillations. It is found to have successive maxima of 2.1 cm and 1.3 cm. If the damping coefficient b is 10 g s − 1 , find the time interval between these two successive maxima. [Given ln ( 2.1/1.3 ) = 0.479 ]

TestHub · Accepted Answer

For damped oscillations the amplitude decays as below.

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

Two successive maxima are separated by one time period $T$ .

$\frac{A _{1}}{A _{2}} = e^{b T /2 m}$

$T = \frac{2 m}{b} ln \frac{A _{1}}{A _{2}} = \frac{2 \times 5}{10} ln \frac{2.1}{1.3} = 0.479$ s

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