Representing and Analyzing SHM
Position in simple harmonic motion is a cosine of time. Velocity is too, and so is acceleration: three sinusoids of the same period, offset from each other in a fixed way. Reading those offsets is most of what this topic asks. Stack the three curves on a common time axis and the rules pop out: $x$ peaks where $v = 0$ and $|a|$ peaks too, $v$ peaks where $x = 0$ and $a = 0$, and $a$ is the upside-down twin of $x$ at every instant.
The classic traps: aligning all three curves so their peaks land at the same instant (they don't), reading zero velocity at a turning point as zero acceleration (the opposite holds; that's where $|a|$ peaks), and reading the slope of $x$-vs-$t$ as acceleration (it's velocity; acceleration is the slope of $v$-vs-$t$). Each trap shows up at least twice in the lesson and the diagnostic, in different forms.
The work
3 ways in · any order
Lesson
Representing and Analyzing SHM
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Build the phase relationships between $x(t)$, $v(t)$, and $a(t)$, then take them through a ten-scenario applet that pins down where each curve peaks and where it crosses zero.
Diagnostic
10-item topic check
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Ten items that test how you read $x$-vs-$t$, $v$-vs-$t$, and $a$-vs-$t$ graphs, and where the slope-vs-area rule swaps as you switch between graph types.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.