A particle moves in a straight line. If u is the velocity at a distance x from a fixed point on the line and $v^{2} = a - {bx}^{2},$ where a and b arc constants, then:
(i) the motion continues along the positive r-direction only
(ii) the motion is simple harmonic
(iii) the particle oscillates with a frequency equal to $\frac{\sqrt{b}}{2 π}$
(iv) the total energy of the particle is ma

Question

Infinity Learn · Accepted Answer

$$v2=a-bx2$$⇒$$2v$$ $$dv=0-b(2x$$  $$dx)$$ ⇒                    $$vdvdx=-bx$$ ⇒                   $$d2xdx2+bx=0$$ ⇒ motion is SHM and ω$$2=b$$⇒$$f=$$ω$$2$$π$$=22$$π

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