Question 330: Oscillations

Question

A body is executing S.H.M. under the action of force having maximum magntude $$50 \mathrm{~N}$$. When its energy is half kinetic and half potential; the magnitude of the force acting on the particle is

Accepted Answer

Potential energy is a half of the total energy
$$\begin{aligned}
& 	herefore \frac{1}{2} \mathrm{~m} \omega^2 x^2=\frac{1}{2}\left[\frac{1}{2} m \omega^2 A^2ight] \
& 	herefore x^2=\frac{A^2}{2} 	ext { or } x=\frac{A}{\sqrt{2}}
\end{aligned}$$
Maximum force $$F_m=\omega^2 \mathrm{~A}$$
Force at a distance $$\mathrm{x}$$ is $$\mathrm{F}^{\prime}=\omega^2 \mathrm{x}$$
$$\begin{aligned}
& 	herefore \frac{F^{\prime}}{F_m}=\frac{x}{A}=\frac{1}{\sqrt{2}} \
& 	herefore F^{\prime}=\frac{F_m}{\sqrt{2}}=\frac{50}{\sqrt{2}}=25 \sqrt{2}
\end{aligned}$$

Answer

$$\frac{25}{\sqrt{2}} \mathrm{~N}$$

Answer

$$50 \mathrm{~N}$$

Answer

$$25 \mathrm{~N}$$

Answer

$$25 \sqrt{2} \mathrm{~N}$$

Oscillations

A body is executing S.H.M. under the action of force having maximum magntude $50 \mathrm{~N}$. When its energy is half kinetic and half potential; the magnitude of the force acting on the particle is

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