Answer
a)$ x(t) = (.125m)cos(42.0t)$
b)$ x(t) = (2.15 cm)sin(4.63t)$
Work Step by Step
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.
