Solution:

Given the SHM equation:

\[
x = 4 \cos(88t + \frac{\pi}{4})
\]

Solution:

1. Frequency: The general form of SHM is \( x = A \cos(\omega t + \phi) \), where \( \omega = 2 \pi f \) (angular frequency).

Here, \( \omega = 88 \).

\[
f = \frac{\omega}{2 \pi} = \frac{88}{2 \pi} = 14 \, \text{Hz}
\]

2. Initial Displacement: The initial displacement \( x_0 \) is the value of \( x \) at \( t = 0 \).

Substitute \( t = 0 \) into the equation:
\[
x_0 = 4 \cos\left(\frac{\pi}{4}\right) = 4 \cdot \frac{\sqrt{2}}{2} = 2 \sqrt{2} \, \text{m}
\]

Answer:
The frequency is  14 Hz, and the initial displacement is \( 2 \sqrt{2} \, \text{m} \).