The Simple Harmonic Motion (SHM) Calculator is a tool designed to compute the displacement of an object from its equilibrium position at any given time within a harmonic motion. It utilizes the formula:
Formula of Simple Harmonic Motion Calculator
x(t) = A * cos(ωt + φ)
Where:
- x(t) represents the displacement of the object from its equilibrium position at time t.
- A stands for the amplitude of the motion.
- ω denotes the angular frequency (where ω = 2πf, and f is the frequency in hertz).
- t signifies the time in seconds.
- φ represents the phase angle representing the initial phase of the motion at t = 0.
General Terms Table:
Here’s a table summarizing commonly searched terms related to Simple Harmonic Motion:
| Term | Definition |
|---|---|
| Amplitude | The maximum displacement from equilibrium. |
| Frequency | The number of oscillations per unit of time. |
| Angular Frequency | The rate of change of angular displacement per unit time. |
| Phase Angle | Initial angle concerning the reference point at t = 0. |
This table aims to assist individuals in understanding and utilizing relevant terms without the need for repetitive calculations.
Example of Simple Harmonic Motion Calculator
Suppose an object undergoes SHM with an amplitude of 5 meters, a frequency of 2 Hz, a time of 3 seconds, and a phase angle of π/4 radians. Substituting these values into the formula x(t) = A * cos(ωt + φ) results in the calculation of the object’s displacement at that specific time.
Most Common FAQs:
Simple Harmonic Motion refers to a type of periodic motion where the restoring force acting on an object is directly proportional to the displacement of the object from its equilibrium position, and it acts towards the equilibrium position.
The amplitude in SHM determines the maximum distance the object moves from its equilibrium position. A larger amplitude signifies a greater maximum displacement.
The phase angle in SHM indicates the initial position of the object concerning the reference point at t = 0. It influences the starting point of the oscillation.