A particle is moving on $$X-axis$$ and has potential energy $$U=2$$−$$20x+5x2$$ joule, where x is position. The particle is released at x $$=$$ $$-3$$. If the mass of the particle is $$0.1$$ kg, then the maximum velocity (in$$ $$ms-1) of the particle is $$25$$β. If amplitude is $$5$$ m, then the value of β is $$__________$$.

Question

A particle is moving on $$X-axis$$ and has potential energy $$U=2$$−$$20x+5x2$$ joule, where x is position. The particle is released at x $$=$$ $$-3$$. If the mass of the particle is $$0.1$$ kg, then the maximum velocity (in$$ $$ms-1) of the particle is $$25$$β. If amplitude is $$5$$ m, then the value of β is $$__________$$.

Infinity Learn · Accepted Answer

$$U=2$$−$$20x+5x2dUdx=$$−$$20+10xF=$$−$$dUdx=20$$−$$10x=$$−$$10(x$$−$$2)$$∴The particle is executing SHM about mean position x $$-$$ $$2$$ $$=$$ $$0$$ or x $$=$$ $$2$$∴ $$k=10$$    ⇒     mω$$2=10$$    ω$$2=10m=100.1=100$$⇒     ω$$=10rads$$−$$1$$    $$vmax=A$$ω$$=5(10)=50ms$$−$$1$$∴     β$$=2$$

Simple harmonic motion

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Simple harmonic motion

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A particle is moving on X-axis and has potential energy U=2−20x+5x2 joule, where x is position. The particle is released at x = -3. If the mass of the particle is 0.1 kg, then the maximum velocity (in ms-1) of the particle is 25β. If amplitude is 5 m, then the value of β is __________.

U=2−20x+5x2dUdx=−20+10xF=−dUdx=20−10x=−10(x−2)∴The particle is executing SHM about mean position x - 2 = 0 or x = 2∴ k=10 ⇒ mω2=10 ω2=10m=100.1=100⇒ ω=10rads−1 vmax=Aω=5(10)=50ms−1∴ β=2

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