A particle is moving on $$x-axis$$ has potential energy $$U=2$$−$$20x+5x2J$$ along $$x-axis$$. The particle is released at x $$=$$ $$-$$ $$3$$. The maximum value of 'x' is $$_________$$.[x is in meters and U is in joule]

Question

A particle is moving on $$x-axis$$ has potential energy $$U=2$$−$$20x+5x2J$$ along $$x-axis$$. The particle is released at x $$=$$ $$-$$ $$3$$. The maximum value of 'x' is $$_________$$.[x is in meters and U is in joule]

Infinity Learn · Accepted Answer

Given that $$U=2$$−$$20x+5x2Interaction$$ force on particle is given $$asF=$$−$$dUdx=20$$−$$10xAs$$ F is linearly varying with $$-x$$, particle is executing SHMAt equilibrium position F $$=$$ $$0$$⇒ $$20$$−$$10x=0$$⇒ $$x=2Since$$ particle is released at x $$=$$ $$-$$ $$3$$, therefore amplitude of particle is $$5$$.It will oscillate about x $$=$$ $$2$$ with an amplitude of $$5$$.⇒ Maximum value of x will be $$7$$.

Simple harmonic motion

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A particle is moving on x-axis has potential energy $U = 2 - 20 x + 5 x^{2}$ J along x-axis. The particle is released at x = - 3. The maximum value of 'x' is _________.
[x is in meters and U is in joule]

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free study material

Simple harmonic motion

Remember concepts with our Masterclasses.

A particle is moving on x-axis has potential energy U=2−20x+5x2J along x-axis. The particle is released at x = - 3. The maximum value of 'x' is _________.[x is in meters and U is in joule]

Ready to Test Your Skills?

free study material

A particle is moving on x-axis has potential energy $U = 2 - 20 x + 5 x^{2}$ J along x-axis. The particle is released at x = - 3. The maximum value of 'x' is _________.
[x is in meters and U is in joule]