botty_12 said:Would i be able to use a mass on the end of a spring? what would the graph look like if so?
The equation for damped harmonic motion is Y=(e^ax) Sin/Cos bx, where Y is the displacement of the object, e is the base of the natural logarithm, a is the damping coefficient, x is the time, Sin/Cos is either sine or cosine function, and b is the frequency of oscillation.
The damping coefficient, a, represents the rate at which the amplitude of the oscillations decreases over time. It is a measure of the amount of energy lost due to friction or other resistive forces.
The frequency of oscillation, b, determines the rate at which the object vibrates. A higher frequency means the object will oscillate more times in a given time period, leading to a faster decrease in amplitude due to damping.
In damped harmonic motion, the amplitude of the oscillations decreases over time due to the presence of a damping force. In undamped harmonic motion, there is no damping force and the amplitude remains constant. However, both types of motion follow the same basic equation: Y=(e^ax) Sin/Cos bx.
The initial displacement and velocity of the object affect the amplitude and phase of the damped harmonic motion. A larger initial displacement will result in a larger amplitude, while a larger initial velocity will result in a larger phase shift. These initial conditions can greatly impact the behavior of the system over time.