Question

An object in simple harmonic motion has a frequency of one fourth oscillation per minute and an amplitude of 3 feet. Write an equation in the form d equals a sine omega t for the​ object's simple harmonic motion where t is in minutes.

Answer 1

Answer:

$d=3\ sin(\dfrac{\pi t}{2})$

Explanation:

It is given that,

Amplitude of the object in simple harmonic motion, A = 3 ft

Frequency, f = 1/4 oscillations per minute

The equation of simple harmonic motion is given by :

$d=A\ sin\omega t$

$\omega$ is the angular frequency of the object.

Since, $\omega=2\pi f$

$\omega=2\pi (1/4)$          

$\omega=\dfrac{\pi}{2}$

$d=3\ sin(\dfrac{\pi t}{2})$

So, the equation of the simple harmonic motion of the object is $d=3\ sin(\dfrac{\pi t}{2})$