AP Physics 1 Practice Questions: Displacement, Velocity, and Acceleration in SHM

📚 Topic Summary

Simple Harmonic Motion (SHM) is a specific type of periodic motion where the restoring force is directly proportional to the displacement and acts in the opposite direction. Key quantities include displacement ($x$), which describes the object's position relative to its equilibrium, velocity ($v$), representing the rate of change of displacement, and acceleration ($a$), indicating the rate of change of velocity. In SHM, these quantities oscillate sinusoidally with a specific angular frequency ($\omega$). Understanding the relationships between $x$, $v$, and $a$ is crucial for analyzing systems like springs and pendulums.

Mathematically, displacement is given by $x(t) = A \cos(\omega t + \phi)$, where $A$ is the amplitude, $\omega$ is the angular frequency, and $\phi$ is the phase constant. Velocity is the derivative of displacement with respect to time, $v(t) = -A\omega \sin(\omega t + \phi)$, and acceleration is the derivative of velocity with respect to time, $a(t) = -A\omega^2 \cos(\omega t + \phi) = -\omega^2 x(t)$.

🧮 Part A: Vocabulary

Match each term with its correct definition:

✍️ Part B: Fill in the Blanks

Simple Harmonic Motion occurs when the restoring force is proportional to the _________ and acts in the _________ direction. The maximum displacement from equilibrium is called the _________. The derivative of displacement with respect to time is _________, and the derivative of velocity with respect to time is _________.

🤔 Part C: Critical Thinking

Consider a mass-spring system undergoing SHM. How would increasing the mass affect the period of oscillation, and why?