Contents
How is the velocity of a spring mass system calculated?
The position and velocity as a function of time for a spring-mass system with m = 1 kg, k = 4 N/m, A = 10 m are shown in Figure 13.1. 2 for two different choices of the phase, ϕ = 0 and ϕ = π / 2. Figure 13.1. 2: Position and velocity as a function of time for a mass-spring system for two different values of the phase, φ.
How to calculate the motion of a spring?
The motion of the spring is clearly periodic. If the period of the motion is T, then the position of the mass at time t will be the same as its position at t + T. The period of the motion, T, is easily found: T = 2π ω = 2π√m k. And the corresponding frequency is given by: f = 1 T = ω 2π = 1 2π√k m.
How is the mass attached to a spring?
The mass is attached to a spring with spring constant k which is attached to a wall on the other end.
Which is the initial condition for the motion of a spring?
ϕ = π / 2 corresponds to the “initial condition” at t = 0, where the position of the mass is x = 0 and its velocity is in the negative direction, and with maximal amplitude. The position is always between x = ± A, and the velocity is always between v = ± Aω . The motion of the spring is clearly periodic.
As before, the spring-mass system can be thought of as representing a single mode of vibration in a real system, whose natural frequency and damping coefficient coincide with that of our spring-mass system. We will consider three types of forcing applied to the spring-mass system, as shown below:
What happens when you change the phase of a spring mass system?
Changing the phase, ϕ, results in an horizontal shift of the functions. A positive phase results in a shift of the functions to the left. The highest speed corresponds to a position of x = 0 and the largest position, x = ± A, corresponds to a speed of zero.
What does linearity mean in mass spring damper?
The mass-spring- damper differential equation is of a special type; it is a linearsecond-order differential equation. In mathematical terms, linearity means that y, dy/dtand d2y/dt2only occur to the power 1 (no y2or (d2y/dt2)3terms, for example). In real-world terms, linearity means “What goes in, comes out”!