The motion of a mass attached to a spring is an example of a vibrating system. The spring (and its spring constant) is fully responsible for force. Consider a spring with mass m with spring constant k, in a closed environment spring demonstrates a simple harmonic motion. In terms of energy, all systems have two types of energy, potential energy and kinetic energy. This is one of the most famous example of differential equation. In this Lesson, the motion of a mass on a spring is discussed in detail as we focus on how a variety of quantities change over the course of time.

Overview of key terms, equations, and skills for the simple harmonic motion of spring-mass systems, including comparing vertical and horizontal springs.
From the above equation, it is clear that the period of oscillation is free from both gravitational acceleration and amplitude. The period of oscillation of a simple pendulum does not depend on the mass of the bob. T = 2π √m/k. What is Spring Mass System? Hand in 2/07/2018. Of course, you may not heard anything about 'Differential Equation' in the high school physics. Energy variation in the spring-damper system . Probably you may already learned about general behavior of this kind of spring mass system in high school physics in relation to Hook's Law or Harmonic Motion. Introduction: In this worksheet we will be exploring the spring/mass system modeled Of primary interest for such a system is its natural frequency of vibration. If the spring itself has mass, its effective mass must be included in . Finding the particular integral • Then do the same for a horizontal spring-mass system Procedure: Work on the following activity with 2-3 other students during class (but be sure to complete your own copy) and nish the exploration outside of class. Introduction All systems possessing mass and elasticity are capable of free vibration, or vibration that takes place in the absence of external excitation. Purpose: To investigate the mass spring systems in Chapter 5.

Given an ideal massless spring, is the mass on the end of the spring. Lecture 2: Spring-Mass Systems Reading materials: Sections 1.7, 1.8 1.
By contrast, the period of a mass-spring system does depend on mass.For a mass-spring system, the mass still affects the inertia, but it does not cause the force. Such quantities will include forces, position, velocity and energy - both kinetic and potential energy. • So the last physical system we are going to look at in this first part of the course is the forced coupled pendula, along with a damping factor 1. Finding the Complementary Function 2.