Question

Pendulum motion is analyzed to estimate simple harmonic motion. A plot is generated with the position of the pendulum over time. The graph is used to find a sinusoidal curve of the form $y=A\cos \left[B\right(x-c\left)\right]+D$. Determine the amplitude, period, and frequency. (Activity 16, Real-World Math with the CBL System.)

Short answer

The amplitude is A, period of function and frequency of function are$\frac{2\mathrm{\pi }}{B}and\frac{B}{2\mathrm{\pi }}$respectively.

Step-by-step solution

Step 1. Given Information

The given function is$y=A\cos \left[B\right(x-c\left)\right]+D$

Step 2. Explanation

The pendulum motion is analyzed to estimate simple harmonic motion given by the function.

In this expression, we have,

'A' as the amplitude of the function, period of the function is $T=\frac{2\mathrm{\pi }}{B}$, phase shift of the function is $\frac{C}{B}$and 'D' controls the vertical shift of the function.

Thus, we get,

The amplitude as 'A', period of function and frequency of function are $\frac{2\mathrm{\pi }}{B}and\frac{B}{2\mathrm{\pi }}$respectively.