The velocity of a particle executing simple harmonic motion along -axis is described as where represents displacement

Question

The velocity of a particle executing simple harmonic motion along $x$ -axis is described as $v^{2} = 50 - x^{2},$ where $x$ represents displacement. If the time period of motion is $\frac{x}{7} s,$ the value of $x$ is ______. [2026]

Smart Achievers · Accepted Answer

(44)

$Given velocity of a particle, v^{2} = 50 - x^{2}$

$x$

$v^{2} = ω^{2} A^{2} - ω^{2} x^{2}$

$∴$ $ω^{2} = 1 \Rightarrow ω = 1$

$Time period T = \frac{2 π}{ω} = \frac{2 π}{1} = 2 π sec$

$Now compare it with \frac{x}{7} = 2 π$

$\Rightarrow x = 2 \times \frac{22}{7} \times 7 = 44$

Solution

Q.
The velocity of a particle executing simple harmonic motion along $x$ -axis is described as $v^{2} = 50 - x^{2},$ where $x$ represents displacement. If the time period of motion is $\frac{x}{7} s,$ the value of $x$ is ______. [2026]

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Solution

Q. The velocity of a particle executing simple harmonic motion along x-axis is described as v2=50-x2, where x represents displacement. If the time period of motion is x7s,the value of x is ______. [2026]

Ans. (44) Given velocity of a particle, v2=50-x2 By comparing this to the standard equation v2=ω2A2-ω2x2 ∴ ω2=1⇒ω=1 Time period T=2πω=2π1=2π sec Now compare it with x7=2π ⇒x=2×227×7=44

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Q.
The velocity of a particle executing simple harmonic motion along $x$ -axis is described as $v^{2} = 50 - x^{2},$ where $x$ represents displacement. If the time period of motion is $\frac{x}{7} s,$ the value of $x$ is ______. [2026]