Two SHM-s are represented by the equations- y1-0-1 sin 100 - t -3 and y2 -0-1 cos 100 - t- The phase difference between the speeds of the two particles is-

Ν_1=dy/dt=0.1 × 100 π cos ( 100 π t +π/3 ) and ν_2 =dy_2/dt= 0.1 × 100 π sin 100 π t =0.1 × 100 π× cos ( 100 π t +π/2 ) ∴ Phase difference between two spee ...

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Standard XIII

Physics

SHM expression

Two SHM’s are...

Question

Two SHM’s are represented by the equations, $y_{1} = 0.1 s i n (100 π t + \frac{π}{3})$ and $y_{2} = 0.1 c o s 100 π t$ . The phase difference between the speeds of the two particles is,

\frac{π}{3}

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\frac{π}{8}

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\frac{π}{6}

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\frac{π}{4}

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Solution

The correct option is C $\frac{π}{6}$
$ν_{1} = \frac{d y}{d t} = 0.1 \times 100 π c o s (100 π t + \frac{π}{3}) a n d ν_{2} = \frac{d y_{2}}{d t} = - 0.1 \times 100 π s i n 100 π t = 0.1 \times 100 π \times c o s (100 π t + \frac{π}{2})$
$∴$ Phase difference between two speeds = $(100 π t + \frac{π}{3}) - (100 π t + \frac{π}{2}) = \frac{π}{3} - \frac{π}{2} = \frac{π}{6}$

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Two SHM’s are represented by the equations, $y_{1} = 0.1 s i n (100 π t + \frac{π}{3})$ and $y_{2} = 0.1 c o s 100 π t$ . The phase difference between the speeds of the two particles is,