A $$4$$ kg particle is moving along the $$x-axis$$ under the action of the force F $$=$$ $$-($$π$$216)xN$$. At t $$=$$ $$2$$ $$sec$$, the particle passes through the origin and at t $$=$$ $$l0$$ $$sec$$ its speed is $$42$$ $$m/s$$. The amplitude of the motion is:

Question

A $$4$$ kg particle is moving along the $$x-axis$$ under the action of the force F $$=$$ $$-($$π$$216)xN$$. At t $$=$$ $$2$$ $$sec$$, the particle passes through the origin and at t $$=$$ $$l0$$ $$sec$$ its speed is $$42$$ $$m/s$$. The amplitude of the motion is:

Infinity Learn · Accepted Answer

a $$=$$ $$-($$π$$264)x$$   ⇒ω $$=$$ π$$264$$ $$=$$ π$$8$$⇒T $$=$$ $$2$$πω $$=$$ $$16$$ $$sec$$.There is a time difference of $$T2$$ between t $$=$$ $$2$$ $$sec$$ to t $$=$$ $$l0$$ $$sec$$. Hence particle is again passing through the mean position of SHM where its speed is maximum.i.e., $$Vmax=$$ Aω $$=$$ $$42$$⇒A $$=$$ $$42$$$$π$$$$8$$ $$=$$ $$322$$$$π$$m.

A 4 kg particle is moving along the x-axis under the action of the force $F = - (\frac{π^{2}}{16}) xN$ . At t = 2 sec, the particle passes through the origin and at t = l0 sec its speed is $4 \sqrt{2}$ m/s. The amplitude of the motion is:

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A 4 kg particle is moving along the x-axis under the action of the force F = -(π216)xN. At t = 2 sec, the particle passes through the origin and at t = l0 sec its speed is 42 m/s. The amplitude of the motion is:

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Ready to Test Your Skills?

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A 4 kg particle is moving along the x-axis under the action of the force $F = - (\frac{π^{2}}{16}) xN$ . At t = 2 sec, the particle passes through the origin and at t = l0 sec its speed is $4 \sqrt{2}$ m/s. The amplitude of the motion is: