Chapter 8.5, Problem 55AYU

To determine

To find: The amplitude, period and frequency.

Answer to Problem 55AYU

The amplitude is $A$ , period is $\frac{2\pi }{B}$ and frequency is $\frac{B}{2\pi }$ .

Explanation of Solution

Given:

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

Calculation:

The pendulum is analysed with simple harmonic motion given by,

  $y=A\cos \left[B\left(x-C\right)\right]+D$

Here, the amplitude of the motion is $A$ .

Consider the period of the function is,

  $T=\frac{2\pi }{B}$

Consider the phase shift of the function is,

  $\frac{C}{B}$

Consider the vertical shift of the function is,

  $D$

Thus, the period of the function is,

  $\frac{2\pi }{B}$

Consider the frequency of the function is,

  $f=\frac{B}{2\pi }$