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Sav [38]
3 years ago
14

Find a model for simple harmonic motion that has an initial displacement (t=0) of 0 inches, an amplitude of 5 inches, and a freq

uency 4/3 cycles per second.
Physics
1 answer:
Svetach [21]3 years ago
7 0

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)}

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