A particle is moving along the $$x-axis$$ under the influence of a force given by F $$=$$ $$-5x$$ $$+$$ $$15$$. At time t $$=$$ $$0$$, the particle is located at x $$=$$ $$6$$ and is having zero velocity. It takes $$0.5$$ seconds to reach the origin for the first time. The mass of the particle is

Question

A particle is moving along the $$x-axis$$ under the influence of a force given by F $$=$$ $$-5x$$ $$+$$ $$15$$. At time t $$=$$ $$0$$, the particle is located at x $$=$$ $$6$$ and is having zero velocity. It takes $$0.5$$ seconds to reach the origin for the first time. The mass of the particle is

Infinity Learn · Accepted Answer

A particle moving in a SHM about $$x=3$$ with amplitude $$3$$ will exhibit a motion similar to that described in the problem.Hence  $$x=3+3cos$$ωt. Also $$T2=0.5$$ ⇒$$T=1$$ ⇒ω$$=2$$π.Therefore force  $$F=md2xdt2=-m$$ω$$2(x-3)=-m$$ω$$2x+3m$$ω$$2$$.Comparing with the equation given in the problem mω$$2=5$$ ⇒ $$m=54$$$$π$$$$2$$.

A particle is moving along the x-axis under the influence of a force given by $F = - 5 x + 15$ . At time t = 0, the particle is located at x = 6 and is having zero velocity. It takes 0.5 seconds to reach the origin for the first time. The mass of the particle is

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A particle is moving along the x-axis under the influence of a force given by F = -5x + 15. At time t = 0, the particle is located at x = 6 and is having zero velocity. It takes 0.5 seconds to reach the origin for the first time. The mass of the particle is

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Ready to Test Your Skills?

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A particle is moving along the x-axis under the influence of a force given by $F = - 5 x + 15$ . At time t = 0, the particle is located at x = 6 and is having zero velocity. It takes 0.5 seconds to reach the origin for the first time. The mass of the particle is