It has a root in ##x/A = 1##, but in that case the distance would be equal to the amplitude, not zeroDale said:##\cos^{-1}## has multiple roots.
Simple harmonic motion is a type of periodic motion in which an object moves back and forth in a straight line with a constant frequency and amplitude. This type of motion is often seen in systems that have a restoring force and no friction, such as a mass on a spring or a pendulum.
In real-world situations, simple harmonic motion can be seen in various systems such as the motion of a pendulum, the vibrations of a guitar string, or the oscillations of a car suspension. It is also used in engineering and design to create stable and efficient systems.
The equation for simple harmonic motion is x = A*sin(ωt + φ), where x is the displacement of the object, A is the amplitude, ω is the angular frequency, and φ is the phase constant. This equation can also be written as x = A*cos(ωt + φ) depending on the starting position of the object.
The period of simple harmonic motion is the time it takes for one complete cycle of motion. It can be calculated using the equation T = 2π/ω, where T is the period and ω is the angular frequency. The period is typically measured in seconds.
The mass and spring constant both play a role in determining the frequency and period of simple harmonic motion. A larger mass will result in a lower frequency and longer period, while a larger spring constant will result in a higher frequency and shorter period. These factors also affect the amplitude of the motion.