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 equation of motion of the particle can be represented by

Question

Infinity Learn · Accepted Answer

The mean position of particle can be found by setting F $$=$$ $$-5x$$ $$+$$ $$15$$ $$=$$ $$0$$, so the mean position lies at x $$=$$ $$3$$. One extreme position is at x:$$6$$. Hence the other extreme positionfor this particle undergoing SHM should be at x $$=$$ $$0$$. Time taken by particle to reach from $$x=6$$ to r $$-$$ $$0$$ is $$0.5$$ second, that is, $$T/2=0.5$$ $$sec$$, hence $$T=1$$ second. Hence the equation of motion is $$x=3+Asin$$⁡ω$$t+$$ϕ$$0)$$ where $$A=3$$,ω$$=2$$π×$$1$$ and ϕ$$0=$$π$$2$$. So $$x=3+3cos$$⁡(2$$$$π$$$$t)

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 equation of motion of the particle can be represented by

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