Chapter 7 - Applications of Trigonometric Functions - Section 7.5 Simple Harmonic Motion; Damped Motion; Combining Waves - 7.5 Assess Your Understanding - Page 574: 8

$y=-4 \ \cos(4t)$

The object starts at the vertical position $y=-a$, and moves in the upward direction. The frequency is given by: $\omega=\dfrac{2\pi}{T}$ So, the function has the form (simple harmonic motion): $y=-a\cdot \cos(\omega t)=-a\cdot \cos(\dfrac{2\pi}{T} t)$. Here, $y=-4 \times \cos (\dfrac{2\pi}{(\pi/2)} \times t)=-4 \ \cos(4t)$