Question

Find a model for simple harmonic motion that has an initial displacement (t=0) of 0 inches, an amplitude of 5 inches, and a frequency 4/3 cycles per second.

Answer 1

Answer:

The equation of simple harmonic motion is $y=5\sin{(8\pi t)}$

Explanation:

Given that,

Amplitude = 5 inches

Frequency $f= \dfrac{4}{3}$

As per the question initial displacement is zero at t = 0 for sine curve.

The displacement is zero so the phase difference will be zero.

We know that,

The general equation of simple harmonic motion

$y=A\sin(\omega t+\phi)$

Where, A = amplitude

$\omega$ = angular frequency

$\phi$ = phase shift

We need to calculate the time period

Using formula of frequency

$f=\dfrac{1}{T}$

$T=\dfrac{1}{f}$

Put the value into the formula

$T=\dfrac{1}{\dfrac{4}{3}}$

$T=\dfrac{3}{4}$

We need to calculate the angular frequency

Using formula of angular frequency

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

$\omega=\dfrac{2\pi\times4}{3}$

Put the value into the general equation

$y=5\sin{(8\pi t)}$

Hence, The equation of simple harmonic motion is $y=5\sin{(8\pi t)}$