Question

In damped oscillation mass is $1kg$ and spring constant $=100N/m$, damping coefficeint$=0.5kg{s}^{-1}$. If the mass displaced by $10cm$ from its mean position then what will be the value of its mechanical energy after $4$ seconds?

• A. $0.67J$
• B. $0.067J$
• C. $6.7J$
• D. $0.5J$

Answer 1

The correct option is B $0.067J$

Given,

Mass, $m=1kg$

Spring constant, $k=100N/m^2$

Damping coefficient, $b=0.5kg/s$

Distance, $x=10cm$

Time, $t=4s$

We know,

The energy for damped oscillation, $E=\frac{1}{2}k{x}^2{e}^{-\frac{bt}{m}}$

$E=\frac{1}{2}\times 100\times 0.01\times e^{-\frac{0.5\times 4}{1}}$

$E=\frac{e^{-2}}{2}=0.067J$

Hence the mechanical energy is $0.067J$