For a particle undergoing simple harmonic motion described by x(t) = (4.5 cm) cos ((3.4 Hz) t)x(t)=(4.5cm)cos((3.4Hz)t) Find the first two times that the particle crosses x(t) = 0.x(t)=0.

Explanation:

No matter the coeficient of the cosine function, the function will always be zero as long as the following is true:

Now:

Rewrite 3.4 as:

So:

Therefore the particle crosses the x-axis (x(t)=0) :

The first time is when n=1, so:

And the second time is when n=2, so:

see earlier