# When Do We Use Each SHM Equation?

• negation
In summary, the two equations described are for waves, with one representing simple harmonic motion and the other being a wave equation. The first equation gives us information about the amplitude, angular frequency, and phase angle, while the second equation includes the wave number and velocity. The second equation should actually be written as y2(x,t) = A sin (kx - ωt) and 2π/k is the wavelength, not the period. The phase angle ø is arbitrary, while the term ωt represents the shift or distance traveled by the wave.
negation
Let's say there are 2 equations: (1) y(x,t) = A sin (ωt - ø) and (2) y2(x,t) = A sin (kx - vt)

When are we interested in one over the other? Obviously, (1) tells us that y is represented in terms of ωt( 2πt/T) and ø. Whereas, (2) produces an equation stating the wave number, k(I tend to look at k as the number of cycles/2π) and if we take 2π/k, we obtain the period, T.
vt gives us the shift/ distance as a function of the speed of the wave and the time over which it travels. vt is also really just ø, isn't it?

The second equation is actually a wave equation while the first is just a SHM equation - there is no x on the right hand side of the first equation. The 2nd equation should actually be written 2(x,t) = A sin (kx - ωt). 2π/k is actually the wavelength, not the period. ø is just an arbitrary constant phase. ωt cannot be identified with a constant phase since it is a function of time.

## 1. What is SHM?

SHM stands for Simple Harmonic Motion, which is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. This motion can be seen in systems such as a mass on a spring or a pendulum.

## 2. What is the equation for SHM?

The equation for SHM is x = Acos(ωt + φ), where x is the displacement, A is the amplitude, ω is the angular frequency, and φ is the phase angle.

## 3. What is the difference between SHM and damped harmonic motion?

The main difference between SHM and damped harmonic motion is the presence of a damping force. In SHM, there is no damping force, so the system will continue to oscillate indefinitely. In damped harmonic motion, there is a damping force that gradually decreases the amplitude of the oscillations until they eventually stop.

## 4. How does changing the amplitude affect the SHM equation?

Changing the amplitude, A, in the SHM equation will affect the maximum displacement of the system. A larger amplitude will result in a larger maximum displacement, while a smaller amplitude will result in a smaller maximum displacement. However, the period and frequency of the motion will not be affected.

## 5. What role does the angular frequency play in the SHM equation?

The angular frequency, ω, determines the rate at which the system oscillates. A larger angular frequency will result in a faster oscillation, while a smaller angular frequency will result in a slower oscillation. The angular frequency is directly proportional to the frequency of the motion, which is the number of oscillations per unit time.

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