A body performs SHM along the straight line segment ABCDE with c as the mid point of segment AE (A$$ and E are the extreme position for the $$SHM). Its kinetic energies at B and D are each one fourth of its maximum value. The length of segment AE is $$2R$$, if the distance between B and, D is found to be xR . The value of x is $$__________$$.

Question

A body performs SHM along the straight line segment ABCDE with c as the mid point of segment AE (A$$ and E are the extreme position for the $$SHM). Its kinetic energies at B and D are each one fourth of its maximum value. The length of segment AE is $$2R$$, if the distance between B and, D is found to be xR . The value of x is $$__________$$.

Infinity Learn · Accepted Answer

When the particle crosses point D, its speed is half of the maximum speed. Given that amplitude is $$2R$$⇒ $$v=vmaxRR2$$−$$x2$$ or  $$vmax2=vmaxRR2$$−$$x2$$ or  $$x=32R$$⇒ Distance $$BD=2x=3R$$ Hence $$x=3$$

Applications of SHM

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Applications of SHM

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When the particle crosses point D, its speed is half of the maximum speed. Given that amplitude is 2R⇒ v=vmaxRR2−x2 or vmax2=vmaxRR2−x2 or x=32R⇒ Distance BD=2x=3R Hence x=3

Ready to Test Your Skills?

free study material