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Potential Energy Formulae

For the x-t e...

Question

For the x-t equation of a particle in SHM along x-axis, Match the following two columns
$x = 2 + 2 cos ω t$

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Solution

$x_{m i n} = 2 - 2 = 0 \to$ extreme position
$x_{m i n} = 2 + 2 = 4 \to$ extern position
Mean position $= \frac{x_{m i n} + x_{m i n}}{2} = 2$
Maximum potential energy is at extreme positions.

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For the x-t equation of a particle in SHM along x-axis, answer the following questions using the columns. $x = 2 + 2 c o s (ω t)$ [Given $\to v$ $\Rightarrow$ velocity, $\to a$ $\Rightarrow$ acceleration ]
$\begin{matrix} C o l u m n I & C o l u m n 2 & C o l u m n 3 (I) & x = 0 & (i) & | \to v | = 0 & (P) & | \to a | = ω^{2} (I I) & x = 2 & (i i) & | \to v | = \sqrt{3} ω & (Q) & | \to a | = 2 ω^{2} (I I I) & x = 3 & (i i i) & | \to v | = 2 ω & (R) & | \to a | = z e r o (I V) & x = 4 & (i v) & | \to v | = ω & (S) & | \to a | = \sqrt{3} ω^{2} \end{matrix}$
Which is the correct combination for motion of the particle at $t = (\frac{T}{6})$ where 'T' is the time period of SHM?

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Q. Mass of a particle is 2 kg. Its displacement-time equation in SHM is

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Q. For the x-t equation of a particle in SHM along x-axis, answer the following questions using the columns.

x = 2 + 2 c o s (ω t)

\to v

\Rightarrow

\to a

\Rightarrow

\begin{matrix} C o l u m n I & C o l u m n 2 & C o l u m n 3 (I) & x = 0 & (i) & | \to v | = 0 & (P) & | \to a | = ω^{2} (I I) & x = 2 & (i i) & | \to v | = \sqrt{3} ω & (Q) & | \to a | = 2 ω^{2} (I I I) & x = 3 & (i i i) & | \to v | = 2 ω & (R) & | \to a | = z e r o (I V) & x = 4 & (i v) & | \to v | = ω & (S) & | \to a | = \sqrt{3} ω^{2} \end{matrix}

Which of the options is correct for extreme position of this SHM?

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