AP Physics C: Mechanics Flashcards: Representing and Analyzing SHM
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
What is the general equation for the position of an object in SHM as a function of time?
The position as a function of time is given by $x=A\cos(\omega t+\phi)$, where A is amplitude, ω is angular frequency, and φ is the phase constant.
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What is the general equation for the position of an object in SHM as a function of time?
The position as a function of time is given by $x=A\cos(\omega t+\phi)$, where A is amplitude, ω is angular frequency, and φ is the phase constant.
What is the second-order differential equation that defines Simple Harmonic Motion (SHM)?
The position of an object in SHM is a solution to the equation $\frac{d^{2}x}{dt^{2}}=-\omega^{2}x$, which relates acceleration to position.
If you are given a graph of an object's position versus time and it is a perfect sinusoid, what characteristics of its motion can you determine?
From a sinusoidal position-time graph, you can determine the object's displacement at any time, as well as derive its velocity and acceleration functions.
What do the variables A, ω, and φ represent in the SHM position equation $x=A\cos(\omega t+\phi)$?
A represents the amplitude (maximum displacement), ω represents the angular frequency, and φ represents the phase constant (which depends on the initial position and velocity).
How does the differential equation for SHM, $\frac{d^{2}x}{dt^{2}}=-\omega^{2}x$, embody the relationship between acceleration and position?
The term $\frac{d^{2}x}{dt^{2}}$ is the mathematical representation of acceleration, so the equation directly states that acceleration is proportional to the negative of the position ($x$).
If you know the position function $x=A\cos(\omega t+\phi)$, how can you determine the object's velocity and acceleration?
The velocity can be found by taking the first time derivative of the position function, and the acceleration can be found by taking the second time derivative.
How is the acceleration of an object in SHM related to its position?
The acceleration is directly proportional to the object's displacement from the equilibrium position and is always directed opposite to the displacement, as shown by $a_{x}=-\omega^{2}x$.
An object in SHM is passing through its equilibrium position ($x=0$). What is its acceleration at this instant?
At the equilibrium position ($x=0$), the acceleration is zero because acceleration is directly proportional to displacement ($a_{x}=-\omega^{2}x$).
An object in SHM is at its maximum positive displacement ($x = +A$). What is its acceleration at this point?
At maximum positive displacement, the acceleration is at its maximum negative value, because the restoring force is strongest and directed toward equilibrium ($a_{x}=-\omega^{2}A$).
What is the physical significance of the negative sign in the equation $a_{x}=-\omega^{2}x$?
The negative sign indicates that the acceleration vector always points in the opposite direction to the displacement vector, which is the defining characteristic of the restoring force in SHM.