A particle is executing SHM with amplitude A . The time taken by the particle to move from x=0 to x=A2is t1and from x=A2 to x = A is t2. Then find the value of t1t2 .

t1 =A/2 A2=A sin(ωt1+0) ωt1=π/6 2πt1T=π/6 t1=T12 t2=T4-T12=T6 t1t2=12

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A particle is executing SHM with amplitude A . The time taken by the particle to move from x=0 to x= $\frac{A}{2} is t_{1} and from x = \frac{A}{2} to x = A is t_{2} . Then find the value of \frac{t_{1}}{t_{2}} .$

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Detailed Solution

$t_{1} = A / 2 \frac{A}{2} = A \sin (ω t_{1} + 0) ω t_{1} = π / 6 \frac{2 π t_{1}}{T} = π / 6 t_{1} = \frac{T}{12} t_{2} = \frac{T}{4} - \frac{T}{12} = \frac{T}{6} \frac{t_{1}}{t_{2}} = \frac{1}{2}$

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