Chapter 8.5, Problem 56AYU

To determine

To find: The amplitude, period and frequency.

Answer to Problem 56AYU

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 $y=A\cos \left[Bx-C\right]$ .

Calculation:

The pendulum is analysed with simple harmonic motion given by,

  $y=A\cos \left[Bx-C\right]$

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,

  $\frac{C}{B}$

Thus, the period of the function is,

  $\frac{2\pi }{B}$

Consider the frequency of the function is,

  $f=\frac{B}{2\pi }$