Solving Simple Harmonic Motion: Oscillatory & Sinusoidal in Time

In summary, Simple Harmonic Motion (SHM) is a type of periodic motion in which a system's displacement from its equilibrium position follows a sinusoidal pattern over time. The equation for SHM is x = A sin(ωt + φ), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, and φ is the phase constant. The period (T) of SHM can be found by taking the inverse of the angular frequency, T = 2π/ω, and the frequency (f) is equal to the inverse of the period, f = 1/T. The amount of damping in a system can affect the natural frequency and period of SHM, with overdamping resulting
  • #1
iurod
51
0
Hi,
I having trouble grasping what: "oscillatory motions are sinusoidal in time" means... does this just mean that when solving a problem for simple harmonic motion that the equation is going to involve both and sin/cos and time? Sorry this might be more of a mathematical question.
 
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  • #2
If you plot the position as a function of time, you'll get a sinusoidal graph. (Yes, descriptions of SHM will involve sines and cosines.)
 

Related to Solving Simple Harmonic Motion: Oscillatory & Sinusoidal in Time

1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion in which a system's displacement from its equilibrium position follows a sinusoidal pattern over time. This means that the system moves back and forth around its equilibrium position in a regular and repeating manner.

2. What is the equation for Simple Harmonic Motion?

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 (related to the system's stiffness), and φ is the phase constant (related to the starting position of the system).

3. How do you solve for the period of Simple Harmonic Motion?

The period (T) of Simple Harmonic Motion can be found by taking the inverse of the angular frequency, T = 2π/ω. This represents the amount of time it takes for one full oscillation (back and forth motion) of the system.

4. What is the relationship between frequency and period in Simple Harmonic Motion?

The frequency (f) of Simple Harmonic Motion is the number of oscillations per unit time and is equal to the inverse of the period, f = 1/T. This means that systems with shorter periods have higher frequencies and vice versa.

5. How does damping affect Simple Harmonic Motion?

Damping is the process of reducing the amplitude of oscillations over time and can affect Simple Harmonic Motion by changing the system's natural frequency and period. Overdamping (large damping) can result in longer periods and underdamping (small damping) can result in shorter periods. Critical damping (optimal amount of damping) results in the system returning to equilibrium in the shortest amount of time.

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