The equation of a particle executing simple harmonic motion is given by x = sin $(t + \frac{1}{3}) m$ . At t = 1s, the speed of particle will be

(Given : p = 3.14)

Option 1 -

0 cm s^-1

Option 2 -

157 cm s^-1

Option 3 -

272 cm s^-1

Option 4 -

314 cm s^-1

2 Views | Posted 3 months ago

Asked by Shiksha User

1 Answer

Answered by

Payal Gupta | Contributor-Level 10

3 months ago

Correct Option - 2

Detailed Solution:

$x = s i n π (t + \frac{1}{3})$

$v = \frac{d x}{d t} = c o s [π (t + \frac{1}{3})] \times π$

$= c o s (π + \frac{π}{3}) \times π$

$= - c o s \frac{π}{3} \times (π)$

$= - \frac{π}{2} = - 1.57 m / s e c$

Speed = 157 cm/sec

<!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1813497314"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mi>x</mi> <mo>=</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>π</mi> <mrow> <mo> (</mo> <mrow> <mi>t</mi> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </math> <math> <mrow> <mi>v</mi> <mo>=</mo> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo> [</mo> <mrow> <mi>π</mi> <mrow> <mo> (</mo> <mrow> <mi>t</mi> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo>×</mo> <mi>π</mi> </mrow> </math> <math> <mrow> <mo>=</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo> (</mo> <mrow> <mi>π</mi> <mo>+</mo> <mfrac> <mrow> <mi>π</mi> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mi>π</mi> </mrow> </math> <math> <mrow> <mo>=</mo> <mo>−</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mfrac> <mrow> <mi>π</mi> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> <mo>×</mo> <mrow> <mo> (</mo> <mrow> <mi>π</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math> <math> <mrow> <mo>=</mo> <mo>−</mo> <mfrac> <mrow> <mi>π</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>.</mo> <mn>5</mn> <mn>7</mn> <mi>m</mi> <mo>/</mo> <mi>s</mi> <mi>e</mi> <mi>c</mi> </mrow> </math>            <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1813497318"> </o:OLEObject></xml><! [endif]-> Speed = 157 cm/sec

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The equation of a particle executing simple harmonic motion is given by x = sin $(t + \frac{1}{3}) m$ . At t = 1s, the speed of particle will be

(Given : p = 3.14)

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The equation of a particle executing simple harmonic motion is given by x = sin $(t + \frac{1}{3}) m$ . At t = 1s, the speed of particle will be

(Given : p = 3.14)