A oscillator of mass 100g executes damped oscillation. When it complete 100 oscillations its amplitude of oscillation becomes half to its original amplitude. If time period is 2s, then find the value of damping coefficient.

Explanation

Here, `m = 100g, T = 2s` for 100 oscillation, `t= 200s, A(t) = (A)/(2)`
Amplitude of damping oscillation at time t.
`A(t)= Ae^((-bt)/(2m))`
`therefore (A)/(2) = Ae^((-bt)/(2m))`
`therefore 2^(-1) = e^((-bt)/(2m))`
`therefore 2 = e^((bt)/(2m))`
`thereforer ln 2 = (bt)/(2m)" "[therefore " taking e based log "]`
`therefore 2.3.03xx log 2 = (b xx 200)/(2xx100)" "[therefore ln2 = 2.303 log 2]`
`therefore 2.303 xx 0.3010 = b`
`therefore b= 0.693`
`therefore b = 0.693 (" dyne "*" second ")/(" cm ")`.