Question 15: Oscillations

Question

A particle executes a linear SHM with an
amplitude of 4 cm. At the mean position the
velocity of the particle is 10 cm/s. What is the
displacement of the particle when its speed
becomes 5 cm/s?

Accepted Answer

Amplitude of the particle is SHM,
A = 4 cm
At mean position velocity,
$v_{\max}=10$ cm/s
$\Rightarrow A\omega=10$
$
\begin{aligned}
\Rightarrow \quad \omega & =\frac{10}{A} \
& =\frac{10}{4}=2.5 \mathrm{rad} / \mathrm{s}
\end{aligned}$
Again when $v=5 \mathrm{~cm} / \mathrm{s}$, then displacement, $x=$ ?
We know that,
$\begin{aligned}
& v=\omega \sqrt{A^2-x^2} \
& \Rightarrow \quad 5=2.5 \sqrt{4^2-x^2} \
& \Rightarrow \quad 2=\sqrt{A^2-x^2} \
& \Rightarrow \quad 4=A^2-x^2 \
& \Rightarrow \quad 4=4^2-x^2 \
& \Rightarrow \quad x^2=16-4=12 \
& 	herefore \quad x=\sqrt{12}=2 \sqrt{3} \mathrm{~cm} \
&
\end{aligned}$

Answer

2($\sqrt3$) cm

Answer

2($\sqrt5$) cm

Answer

$\sqrt5$ cm

Answer

$\sqrt3$ cm

Oscillations

A particle executes a linear SHM with an amplitude of 4 cm. At the mean position the velocity of the particle is 10 cm/s. What is the displacement of the particle when its speed becomes 5 cm/s?

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