A spring mass system executes damped harmonic oscillations given … - Vidyadip

Question

A spring mass system executes damped harmonic oscillations given by the equation

$y = A{e^{ - \frac{{bt}}{{2m}}}}\sin (\omega 't + \phi )$

where the symbols have their usual meanings. If a $2\ kg$ mass $(m)$ is attached to a spring of force constant $(K)$ $1250\ N/m$ , the period of the oscillation is $\left( {\pi /12} \right)s$ . The damping constant $‘b’$ has the value. ..... $kg/s$

✓

Answer

d
$\omega^{\prime}=\sqrt{\frac{\mathrm{K}}{\mathrm{m}}-\frac{\mathrm{b}^{2}}{4 \mathrm{m}^{2}}}$ and $\omega^{\prime}=\frac{2 \pi}{\mathrm{T}}$

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