Right!NanoTech said:Kinda. I see that [tex] f = \frac{1}{T}[/tex]
Don't do that! Instead write the equation for ω (which is given) in terms of T. (I know you can do it, since that's what you just did to rewrite that equation.)So, from that, I can write:
[tex] x = Acos(\frac{2\pi}{T}(t) + \phi)[/tex]
Simple Harmonic Motion (SHM) is a type of periodic motion in which the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction of the displacement. This means that the object will oscillate back and forth around the equilibrium position in a predictable pattern.
Some common examples of Simple Harmonic Motion include a mass-spring system, a pendulum, and a simple pendulum (e.g. a swing). These systems exhibit SHM because the restoring force (gravity or the spring) is directly proportional to the displacement from the equilibrium position.
The equation for Simple Harmonic Motion is x = A*sin(ωt + φ), where x is the displacement from equilibrium, A is the amplitude (maximum displacement), ω is the angular frequency, and φ is the initial phase angle.
The period (T) of Simple Harmonic Motion is the time it takes for one complete oscillation, while frequency (f) is the number of oscillations per unit time. The relationship between the two is T = 1/f, meaning that as the frequency increases, the period decreases and vice versa.
Damping is the gradual decrease of amplitude over time in a Simple Harmonic Motion system. It can be caused by external forces (such as friction) or internal factors (such as air resistance). Damping decreases the total energy of the system, resulting in a shorter period and smaller amplitude. Eventually, the system will reach equilibrium and stop oscillating.