7 Oscillations

Describe simple harmonic motion.

• Simple harmonic motion is a special case of periodic motion.
• 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: x
  • i. A restoring force is a force that is exerted in a direction opposite to the object’s displacement from an equilibrium position.
  • ii. An equilibrium position is a location at which the net force exerted on an object or system is zero.
  • 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. TOPIC 7.1 Defining Simple Harmonic Motion (SHM)

Describe the frequency and period of an object exhibiting SHM. TOPIC 7.2 Frequency and Period of SHM

• The period of SHM is related to the frequency f of the object’s motion by the following equation: 1T= f
  • i. The period of an object–ideal-spring oscillator is given by the equation
  • ii. The period of a simple pendulum displaced by a small angle is given by the equation AP Physics 1: Algebra-Based Course and Exam Description Oscillations UNIT 7

Describe the displacement, velocity, and acceleration of an object exhibiting SHM. TOPIC 7.3 Representing and Analyzing SHM

• For an object exhibiting SHM, the displacement of that object measured from its equilibrium position can be represented by the equations xA =co s2() ft or xA =si n2() .
  • i. Minima, maxima, and zeros of displacement, velocity, and acceleration are features of harmonic motion.
  • 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.
• Changing the amplitude of a system exhibiting SHM will not change the period of that system.
• Properties of SHM can be determined and analyzed using graphical representations.

Describe the mechanical energy of a system exhibiting SHM.

• The total energy of a system exhibiting SHM is the sum of the system’s kinetic and potential energies. Relevant equation: EUtotal =+K
• Conservation of energy indicates that the total energy of a system exhibiting SHM is constant.
• The kinetic energy of a system exhibiting SHM is at a maximum when the system’s potential energy is at a minimum.
• The potential energy of a system exhibiting SHM is at a maximum when the system’s kinetic energy is at a minimum.
  • i. The minimum kinetic energy of a system exhibiting SHM is zero.
  • 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: Ek= 1 total A2 2 TOPIC 7.4 Energy of Simple Harmonic Oscillators