Question

1. for an object moving in simple harmonic motion with displacement d = 0.5 sin(\frac{\pi}{4} t), find the amplitude a, period p, and frequency f.

a =
p =
f =

Explanation:

Step1: Identify amplitude

The standard form is $d = A\sin(\omega t)$. Here, $A = 0.5$.

Step2: Calculate period

Period $P = \frac{2\pi}{\omega}$. $\omega = \frac{\pi}{4}$, so $P = \frac{2\pi}{\pi/4} = 8$.

Step3: Calculate frequency

Frequency $f = \frac{1}{P} = \frac{1}{8}$.

Answer:

$A = 0.5$
$P = 8$
$f = \frac{1}{8}$