AP Physics 1 - Horizontal Spring Block Oscillators

This paragraph introduces the concept of horizontal spring block oscillators and outlines the objectives of the lesson. The speaker, Dan Fullerton, explains that the focus will be on applying the relationship between frequency, angular frequency, and period, identifying minima, maxima, and zeros of displacement, velocity, and acceleration for a spring block oscillator, determining the total energy of an object undergoing simple harmonic motion, and sketching graphs of kinetic and potential energies as functions of time or displacement. The paragraph also describes the setup of a spring block oscillator, consisting of a block of mass M on a frictionless surface, attached to a vertical wall by an ideal spring with spring constant K. The angular frequency of the block's oscillation is derived from its mass and the spring constant, and from this, the period of oscillation is calculated. A sample problem is presented to calculate the period, frequency, and angular frequency for a 5 kg block attached to a 2000 N/m spring, displaced by 8 cm from its equilibrium position.

In this paragraph, the speaker discusses how to rank different spring block oscillators by their period of oscillation. A method is provided for determining the period using the formula T = 2π√(M/K). The speaker then poses a challenge to the audience to find the periods for four different systems labeled A, B, C, and D. After a pause for the audience, the speaker returns to rank the systems from longest to shortest period. The paragraph continues with an in-depth analysis of energy in a spring block oscillator, emphasizing that the total energy remains constant during simple harmonic motion, with a continuous transfer between kinetic and potential energy. The speaker describes the energy dynamics at the equilibrium position and at maximum amplitude positions, highlighting that at equilibrium, all energy is kinetic, while at maximum amplitude, all energy is potential. A graphical representation of position, velocity, potential energy, and force is used to illustrate these concepts.

This paragraph delves deeper into the analysis of a horizontal spring block oscillator, focusing on displacement, velocity, stored elastic potential energy, kinetic energy, net force, and acceleration. The speaker explains how these quantities vary at different points during the oscillation cycle. At points of maximum displacement (B and C), the velocity is zero, and the energy is entirely potential, while at the equilibrium position (A), the energy is all kinetic. The speaker then addresses a sample problem involving a 2 kg block attached to a spring with a force constant of 20 N/m, stretched to a displacement of 50 cm. The spring constant is calculated using Hooke's law, and the total energy is determined using the displacement and spring constant. The speed of the block at equilibrium and at various positions is calculated, demonstrating how velocity changes with position. The acceleration at the equilibrium point and at a displacement of 50 cm is also calculated, using Newton's second law and Hooke's law. The net force on the block at equilibrium and at a displacement of 25 cm is determined. Finally, the speaker finds the position where the kinetic energy equals the elastic potential energy of the spring, highlighting that this point is not midway between the equilibrium position and the maximum displacement position.

The speaker concludes the lesson on simple harmonic motion in horizontal spring block oscillators by summarizing the key points discussed. The importance of understanding the conservation of energy, the relationship between kinetic and potential energy, and the dynamics of displacement, velocity, and acceleration is emphasized. The speaker encourages the audience to seek further help or ask questions on the topic and wishes everyone a great day. The paragraph ends with a prompt for additional resources on the topic, directing the audience to a website for more information.