AP®︎ Physics 1: Unit 7 Practice Test

Essential Knowledge: 7.1.A.1

Simple harmonic motion is a special case of periodic motion.

Essential Knowledge: 7.1.A.2

SHM results when the magnitude of the restoring force exerted on an object is proportional to that object’s displacement from its equilibrium position. Derived equation: $ma_x = -k\Delta x$

Essential Knowledge: 7.1.A.2.i

A restoring force is a force that is exerted in a direction opposite to the object’s displacement from an equilibrium position.

Essential Knowledge: 7.1.A.2.ii

An equilibrium position is a location at which the net force exerted on an object or system is zero.

Essential Knowledge: 7.1.A.2.iii

The motion of a pendulum with a small angular displacement can be modeled as simple harmonic motion because the restoring torque is proportional to the angular displacement.

Essential Knowledge: 7.2.A.1

The period of SHM is related to the frequency $f$ of the object’s motion by the following equation: $T = \frac{1}{f}$

Essential Knowledge: 7.2.A.1.i

The period of an object–ideal-spring oscillator is given by the equation $T_s = 2\pi\sqrt{\frac{m}{k}}$.

Essential Knowledge: 7.2.A.1.ii

The period of a simple pendulum displaced by a small angle is given by the equation $T_p = 2\pi\sqrt{\frac{\ell}{g}}$.

Essential Knowledge: 7.3.A.1

For an object exhibiting SHM, the displacement of that object measured from its equilibrium position can be represented by the equations $x = A\cos(2\pi ft)$ or $x = A\sin(2\pi ft)$.

Essential Knowledge: 7.3.A.1.i

Minima, maxima, and zeros of displacement, velocity, and acceleration are features of harmonic motion.

Essential Knowledge: 7.3.A.1.ii

Recognizing the positions or times at which the displacement, velocity, and acceleration for SHM have extrema or zeros can help in qualitatively describing the behavior of the motion.

Essential Knowledge: 7.3.A.2

Changing the amplitude of a system exhibiting SHM will not change the period of that system.

Essential Knowledge: 7.3.A.3

Properties of SHM can be determined and analyzed using graphical representations.

Essential Knowledge: 7.4.A.1

The total energy of a system exhibiting SHM is the sum of the system’s kinetic and potential energies. Relevant equation: $E_{\text{total}} = U + K$

Essential Knowledge: 7.4.A.2

Conservation of energy indicates that the total energy of a system exhibiting SHM is constant.

Essential Knowledge: 7.4.A.3

The kinetic energy of a system exhibiting SHM is at a maximum when the system’s potential energy is at a minimum.

Essential Knowledge: 7.4.A.4

The potential energy of a system exhibiting SHM is at a maximum when the system’s kinetic energy is at a minimum.

Essential Knowledge: 7.4.A.4.i

The minimum kinetic energy of a system exhibiting SHM is zero.

Essential Knowledge: 7.4.A.4.ii

Changing the amplitude of a system exhibiting SHM will change the maximum potential energy of the system and, therefore, the total energy of the system. Relevant equation for a spring–object system: $E_{\text{total}} = \frac{1}{2}kA^2$