What is the equation of motion for a simple harmonic oscillator with amplitude A

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Question: What is the equation of motion for a simple harmonic oscillator with amplitude A and angular frequency ω?

Options:

Correct Answer: x(t) = A cos(ωt)

Solution:

The equation of motion for SHM is x(t) = A cos(ωt) or x(t) = A sin(ωt).

What is the equation of motion for a simple harmonic oscillator with amplitude A and angular frequency ω?

What is the equation of motion for a simple harmonic oscillator with amplitude A and angular frequency ω?

Step 1: Understand that a simple harmonic oscillator (SHO) is a system that moves back and forth in a regular pattern.
Step 2: Recognize that the motion can be described using a mathematical equation.
Step 3: Identify the two key parameters: amplitude (A) and angular frequency (ω).
Step 4: Amplitude (A) is the maximum distance from the center position (equilibrium).
Step 5: Angular frequency (ω) relates to how fast the oscillator moves back and forth.
Step 6: The equation of motion can be expressed in two forms: using cosine or sine.
Step 7: The cosine form is x(t) = A cos(ωt), where x(t) is the position at time t.
Step 8: The sine form is x(t) = A sin(ωt), which is another way to describe the same motion.
Step 9: Both equations represent the same simple harmonic motion but start at different points.

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