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Wave Equation

In what time ...

Question

In what time after its motion begins, will a particle oscillating according to the equation $x = 5 c o s 0.2 π t$ move from the mean position to maximum displacement position?

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Solution

At mean position,
$x = 0$
$5 cos (0.2 π t_{1}) = 0$
$0.2 π t_{1} = π / 2$
$t_{1} = 2.5 s$

At extreme position,
$x = - 5$
$5 cos (.2 π t_{2}) = - 5$
$.2 π t_{2} = π$
$t_{2} = 5 s$

Time taken is $2.5 s$

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