A particle is subjected to two simple harmonic motions given by, y1=10 sin ωt, y2= 5 sin ωt+π. The maximum speed of the particle is:

A particle is subjected to two simple harmonic motions given by, $y_{1} = 10 \sin ωt, y_{2} = 5 \sin (ωt + π)$ . The maximum speed of the particle is:

A
$\sqrt{10^{2} + 5^{2}} ω$
B
$\sqrt{10^{2} - 5^{2}} ω$
C
$5 ω$
D
$15 ω$

Solution:

$y = y_{1} + y_{2} = 10 \sin ωt + 5 \sin (ωt + π) = 10 \sin ωt - 5 \sin ωt Velocity = \frac{dy}{dt} = 5 ω \cos ωt \Rightarrow maximum speed = 5 ω$

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