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How do you calculate the displacement in simple harmonic motion at a given time?

To calculate the displacement in simple harmonic motion at a given time, use the equation x = A cos(ωt + φ).

In simple harmonic motion, an object oscillates back and forth around an equilibrium position with a constant amplitude and period. The displacement of the object at any given time can be calculated using the equation x = A cos(ωt + φ), where x is the displacement, A is the amplitude, ω is the angular frequency (ω = 2πf, where f is the frequency), t is the time, and φ is the phase angle.

To use this equation, first determine the values of A, ω, and φ. A is the maximum displacement from the equilibrium position, which can be measured or given in the problem. ω can be calculated using the period of the motion (T = 1/f) and the formula ω = 2π/T. Finally, φ is the initial phase angle, which can also be given in the problem or determined from the initial conditions.

Once these values are known, simply plug them into the equation x = A cos(ωt + φ) and solve for x at the given time t. This will give the displacement of the object at that particular moment in the simple harmonic motion.

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