A mass of 2 kg is attached to the spring of spring constant 50 Nm^-1. The block is pulled to a distance of 5cm from its equilibrium position at x = 0 on a horizontal frictionless surface from rest at t = 0. Write the expression for its displacement at anytime t.

This is a short answer type question as classified in NCERT Exemplar

Consider the diagram of the spring block system. It is a SHM with amplitude of 5cm about the mean position

Spring constant k=50N/m

Mass =2kg

Angular frequency w= $\sqrt[]{\frac{k}{w}}=\sqrt[]{\frac{50}{2}}=5rad/s$

Y (t)= Asin (wt+ $\varnothing$ )

Y (0)=Asin (w $\times 0+\varnothing$ )

sin $\varnothing$ =1 $\varnothing =\frac{\pi }{2}$

y (t)=Asin (wt+ $\frac{\pi }{2})$ = Acoswt

A=5cm w=5rad/s

Y=5sin5t

<p><span data-teams="true">This is a short answer type question as classified in NCERT Exemplar</span></p><p>Consider the diagram of the spring block system. It is a SHM with amplitude of 5cm about the mean position</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745558603phpG149de_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745558603phpG149de.jpeg" alt="" width="304" height="158"></picture></div><div><p>Spring constant k=50N/m</p><p>Mass =2kg</p><p>Angular frequency w=<span contenteditable="false"> <math> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi>k</mi> </mrow> </mrow> <mrow> <mrow> <mi>w</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>50</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mn>5</mn> <mi>r</mi> <mi>a</mi> <mi>d</mi> <mo>/</mo> <mi>s</mi> </math> </span></p><p>Y (t)= Asin (wt+ <span contenteditable="false"> <math> <mi>∅</mi> </math> </span>)</p><p>Y (0)=Asin (w<span contenteditable="false"> <math> <mo>×</mo> <mn>0</mn> <mo>+</mo> <mi>∅</mi> </math> </span> )</p><p>sin <span contenteditable="false"> <math> <mi>∅</mi> </math> </span>=1<span contenteditable="false"> <math> <mi>∅</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> </span></p><p>y (t)=Asin (wt+<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mo>)</mo> <mi> </mi> </math> </span> = Acoswt</p><p>A=5cm w=5rad/s</p><p>Y=5sin5t</p></div></div>

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