Simple Harmonic Motion equation rearrangement?

In summary, the equation for Simple Harmonic Motion is x = A sin(ωt + φ). To solve for amplitude, rearrange the equation to A = x/sin(ωt + φ). This equation can be used for any type of oscillating motion that follows the characteristics of simple harmonic motion. The period of oscillation can be calculated using the equation T = 2π/ω, and there is no limit to the amplitude in Simple Harmonic Motion, but it should be smaller than the wavelength for accuracy.
  • #1
spacealgae
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Homework Statement


Hello! I have a physics homework question I just need help at!
What I am supposed to do is calculate the value for free-fall acceleration, ag, for each of my trials that I did in my lab. I supposed to use the equation for the period of the simple pendulum, T=2π√l/g, but I have to rearrange it to solve for ag. How would I do that?

Homework Equations


Here are some sample values I used in my lab:
Length: 1 meter
Period: 20.1 seconds

The Attempt at a Solution

 
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  • #2
*Update*
I figured it out!
 

1. 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, A is the amplitude, ω is the angular frequency, and φ is the phase angle.

2. How do I rearrange the Simple Harmonic Motion equation to solve for amplitude?

To solve for amplitude, you can rearrange the equation to A = x/sin(ωt + φ). This will give you the value of the amplitude at any given time t.

3. Can the Simple Harmonic Motion equation be used for any type of oscillating motion?

Yes, the Simple Harmonic Motion equation can be used for any type of oscillating motion, as long as it follows the characteristics of simple harmonic motion, such as a restoring force proportional to displacement.

4. How do I calculate the period of oscillation using the Simple Harmonic Motion equation?

The period of oscillation can be calculated using the equation T = 2π/ω, where T is the period and ω is the angular frequency. The angular frequency can be found by rearranging the equation to ω = 2π/T.

5. Is there a limit to the amplitude in Simple Harmonic Motion?

No, there is no limit to the amplitude in Simple Harmonic Motion. However, for the equation to accurately describe the motion, the amplitude should be smaller than the wavelength of the motion.

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