## Essential University Physics: Volume 1 (3rd Edition)

a)$x(t) = (.125m)cos(42.0t)$ b)$x(t) = (2.15 cm)sin(4.63t)$
Here, we know that we must use the equation: $$x(t)=Acos( \omega t + \phi)$$ Where omega is the angular frequency, A is the amplitude, and phi is the phase constant. We know: $$\omega = 2 \pi f$$ a) $\omega = 2 \pi (6.68 Hz)$ b) $\omega = 2 \pi (4.63 Hz)$ Using these two results, we get the answer: a)$x(t) = (.125m)cos(42.0t)$ b)$x(t) = (2.15 cm)sin(4.63t)$ Note, the fact that one function is a cosine function while the other is the sine function reflects the phase difference.