Introduction
In physics, simple harmonic motion (SHM) is a type of periodic motion or oscillation motion where the restoring force is proportional to the displacement. This type of motion can be seen in many physical phenomena such as a mass-spring system, pendulum, or an object bouncing up and down on a spring. However, not all periodic motions represent SHM. In this article, we will discuss which of the following expressions does not represent SHM.
Expressions Representing SHM
The following expressions represent simple harmonic motion:
1. x(t) = A cos(ωt + φ)
Where x(t) is the displacement, A is the amplitude, ω is the angular frequency, and φ is the phase angle. This formula represents the motion of a particle oscillating back and forth in a straight line with the restoring force proportional to the displacement.
2. θ(t) = θ0 cos(ωt)
This formula represents the motion of a pendulum, where θ(t) is the angular displacement, θ0 is the maximum angular displacement, ω is the angular frequency, and t is the time. The restoring force is provided by gravity, which is proportional to the displacement of the pendulum.
Expression Not Representing SHM
The following expression does not represent simple harmonic motion:
1. y(t) = e-atsin(b)
Where y(t) is the vertical displacement of the object, e is Euler’s number, a is a damping factor, t is the time, and b is the angular frequency. This expression represents the motion of a damped oscillator, which is an oscillator with a damping force that dissipates energy from the system. The movement of the object will eventually stop due to the loss of energy. Therefore, it does not satisfy the condition for simple harmonic motion.
Conclusion
In conclusion, simple harmonic motion is a common phenomenon observed in many physical systems. The restoring force proportional to the displacement and the system’s motion is periodic. The formulae for SHM are used in many areas of science and engineering. However, some expressions do not represent SHM, such as the damped oscillator. Knowing which expressions represent SHM is essential in understanding periodic motion and its applications in different fields.
