Question

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36 . A particle of mass m is attached to a spring of spring constant 'k' and has a natural frequency $\mathrm{\omega }$₀ . An external force F (t) proportional to cos $\mathrm{\omega }$t $\left(\mathrm{\omega }\ne {\mathrm{\omega }}_0\right)$ is applied to the oscillator. The maximum displacement of the oscillator will be proportional to
$$\begin{gathered} \left(1\right)\frac{m}{{{\omega }_0}^2+{\omega }^2}\left(2\right)\frac{1}{m\left({{\omega }_0}^2-{\omega }^2\right)} \\ \left(3\right)\frac{1}{m\left({{\omega }_0}^2+{\omega }^2\right)}\left(4\right)\frac{m}{\left({{\omega }_0}^2-{\omega }^2\right)} \end{gathered}$$

Answer 1

$$\begin{gathered} accnduetoexternalforcea\text{'}=\frac{\cos \omega t}{m} \\ k=m{{\omega }_0}^2 \\ netaccn \\ a=\left({{\omega }_0}^2+{\omega }^2\right)x \\ x=\frac{a}{\left({{\omega }_0}^2+{\omega }^2\right)} \\ atextremepositiona=1/m \\ amplitude=\frac{1}{m\left({{\omega }_0}^2+{\omega }^2\right)} \\ Regards \end{gathered}$$