Question

an object moves in simple harmonic motion described by the equation d = 4 cos 2πt, where t is measured in seconds and d in inches. find the following.
a. the maximum displacement
b. the frequency
c. the time required for one cycle

Explanation:

Step1: Recall max - displacement formula

For $d = A\cos(\omega t)$, the maximum displacement is $|A|$. In $d = 4\cos(2\pi t)$, $A = 4$.

Step2: Recall frequency formula

The general form is $d=A\cos(\omega t)$, and the frequency $f=\frac{\omega}{2\pi}$. Here $\omega = 2\pi$, so $f=\frac{2\pi}{2\pi}=1$.

Step3: Recall period formula

The period $T$ (time for one - cycle) is given by $T=\frac{2\pi}{\omega}$. Since $\omega = 2\pi$, $T = 1$.

Answer:

a. 4 in.
b. 1 cycles per second
c. 1 s