y = A sin(ωx + φ)

$A$ is the amplitude (peak height), $\omega$ is the angular frequency (radians per unit $x$) and $\phi$ is the phase shift. The period is $T = 2\pi/\omega$ and the wave repeats forever. This is the prototype for every periodic phenomenon in physics.

Slide $A$, $\omega$ and $\phi$ independently and watch the wave stretch vertically, squeeze horizontally and slide left or right. Try $A = 2$, $\omega = 2$, $\phi = \pi/2$ — you get a cosine. The lab shows the period $T$ live so the algebra-to-graph link clicks.

Simple harmonic motion has identical algebra, just with $t$ instead of $x$. So a spring-mass system bobbing 5 cm with period 2 s gives $A = 5$ cm and $\omega = \pi$ rad/s. Mastering this lab speeds up oscillation problems in both Physics and Maths.

Writing $A\sin(\omega(x - x_0))$ shows the curve is shifted by $x_0 = -\phi/\omega$. So $\phi = \pi/2$ with $\omega = 1$ pushes the graph left by $\pi/2$. Students often confuse the sign — the lab flips the wave so you see whether you went left or right.