# Find a function that models the simple harmonic motion having the given properties. Assume that...

## Question:

Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time {eq}t=0 {/eq}, amplitude {eq}6.55in {/eq}, frequency {eq}40Hz {/eq}.

## Simple harmonic motion

We know that the path og simple harmonic motion is modeled as cosinusoida. Since harmonic motion is periodical along the time the trigonometric functions are natural model for this phenomenon. Similarly, we obtain the equations for velocity and acceleration of the simple harmonic motion.

The general form of the equation that models the simple harmonic motion is

$$\omega=A\cos(\omega t + \omega_0)$$

Since the maximum of displacement is reached at {eq}t=0 {/eq}, we conclude that {eq}\omega_0=0 {/eq}. If we put the amplitude and frequency values into the eqution, we obtain:

$$y(t)=6.55\cos(40t)$$