Question 346: Oscillations

Question

A particle is suspended from a vertical spring which is executing S.H.M. of frequency $$5 \mathrm{~Hz}$$. The spring is unstretched at the highest point of oscillation. Maximum speed of the particle is $$(\mathrm{g} =10 \mathrm{~m} / \mathrm{s}^2)$$

Accepted Answer

At the highest point the particle will come to rest momentarily, hence it is at extreme position and has maximum force and acceleration. Since the spring is unstretched, the restoring forceto provided by the weight of the particle
$$	herefore \mathrm{mA} \omega^2=\mathrm{mg}
$$
or $$A \omega^2=\mathrm{g}$$
$$\begin{aligned}
	herefore A & =\frac{g}{\omega^2} \
\omega & =2 \pi f=2 \pi 	imes 5=10 \pi \
	herefore A & =\frac{10}{100 \pi^2}=\frac{1}{10 \pi^2} \
V_{\max } & =A \omega=\frac{1}{10 \pi^2} 	imes 10 \pi=\frac{1}{\pi}\end{aligned}$$

Answer

$$\frac{1}{\pi} \mathrm{m} / \mathrm{s}$$

Answer

$$\frac{1}{4 \pi} \mathrm{m} / \mathrm{s}$$

Answer

$$\frac{1}{2 \pi} \mathrm{m} / \mathrm{s}$$

Answer

$$ \pi~ \mathrm{m} / \mathrm{s}$$

Oscillations

A particle is suspended from a vertical spring which is executing S.H.M. of frequency $5 \mathrm{~Hz}. The spring is unstretched at the highest point of oscillation. Maximum speed of the particle is (\mathrm{g} =10 \mathrm{~m} / \mathrm{s}^2)

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