The amplitude of a damped oscillator decrease | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The amplitude of a damped oscillator at time $t$ is given by $A(t) = A_0 e^{-kt}$.Given that at $t = 5 \ s$,$A(5) = 0.9 A_0$.Substituting this int

Vedclass · Accepted Answer

$0.729$

Vedclass · Answer

(C) The amplitude of a damped oscillator at time $t$ is given by $A(t) = A_0 e^{-kt}$.Given that at $t = 5 \ s$,$A(5) = 0.9 A_0$.Substituting this into the equation: $0.9 A_0 = A_0 e^{-k(5)} \Rightarrow e^{-5k} = 0.9$.We need to find the amplitude after another $10 \ s$,which means at total time $t = 5 + 10 = 15 \ s$.$A(15) = A_0 e^{-k(15)} = A_0 (e^{-5k})^3$.Substituting the value of $e^{-5k} = 0.9$:$A(15) = A_0 (0.9)^3 = A_0 (0.729)$.Thus,$\alpha = 0.729$.

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5 \ s$. In another $10 \ s$,it will decrease to $\alpha$ times its original magnitude,where $\alpha$ equals:

Similar Questions

Which of the following substances is known as $Oil$ $of$ $Wintergreen$?

In Young's double slit experiment,the wavelength of red light is $7800 \, \mathring{A}$ and that of blue light is $5200 \, \mathring{A}$. The value of $n$ for which the $n^{th}$ bright band due to red light coincides with the $(n + 1)^{th}$ bright band due to blue light is:

Which of the following oxides is the most basic oxide?

Suppose there is a hole in a copper plate. On heating the plate,the diameter of the hole would:

How many atoms of calcium will be deposited from a solution of $CaCl_2$ by a current of $25 \ mA$ flowing for $60 \ s$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module