A particle undergoes two simple harmonic motions described by x_1 =...

The total displacement of the particle is given by the principle of superposition:

$x = x_1 + x_2$

Substituting $t = 0.025$ s into the equations for $x_1 and$x_2$:<br><br>$x_1 = 2.0 \sin(100 \pi \times 0.025) = 2.0 \sin(2.5 \pi)$<br><br>$x_1 = 2.0 \sin$\left(2\pi + \dfrac{\pi}{2}\right) = 2.0 \sin\left(\dfrac{\pi}{2}\right) = 2.0 \times 1 = 2.0 \text{ cm}$

x_2 = 2.0 \sin \left(120 \pi \times 0.025 +\dfrac{\pi}{3}\right) =2.0 \sin\left(3\pi +\dfrac{\pi}{3}\right)

$x_2 = 2.0 \left(-\$sin\dfrac{\pi}{3}\right) = -$2.0 \times $\dfrac{\sqrt{3}}{2} = -\sqrt{3} \approx -$1.732 \text{ cm}$<br><br>The net displacement at$t = 0.025$s is:<br><br>$x = 2.0 - 1.732 = 0.268 \text{ cm} \approx 0.27 \text{ cm}