(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Write expressions for simple harmonic motion (a) with amplitude 10 cm, frequency 5.0 Hz, and maximum displacement at t=0; and (b) with amplitude 2.5 cm, angular frequency 5.0 1/s, and maximum velocity at t=0.

2. Relevant equations

[tex]

\begin{gathered}

x(t) = A\cos (\omega t + \varphi ) \hfill \\

\omega = 2\pi f \hfill \\

f = \frac{1}

{T} \hfill \\

\end{gathered}

[/tex]

3. The attempt at a solution

(a)

A=10 cm

f=5.0 Hz

Since the amplitude equals the max displacement at a given t(in this instance t=0), this tells us that the phase angle is zero. So our equation should be....?

[tex]

x(t) = (10cm)\cos \left[ {(10\pi s^{ - 1} )t} \right]

[/tex]

(b)

A=2.5 cm

w=5.0 s^-1

[tex]

\begin{gathered}

V(x) = - A\omega \sin (\omega t + \varphi ) \hfill \\

V(0) = A\omega = V_{\max } \hfill \\

V(0) = - A\omega \sin (\varphi ) \hfill \\

A\omega = - A\omega \sin (\varphi ) \hfill \\

- 1 = \sin (\varphi ) \hfill \\

\varphi = \tfrac{{3\pi }}

{2} \hfill \\

\end{gathered}

[/tex]

So.....?

[tex]

x(t) = (2.5cm)\cos \left[ {(5.0s^{ - 1} )t + \tfrac{{3\pi }}

{2}} \right]

[/tex]

Do these look right? Here is what my answer book gives:

[tex]

\begin{gathered}

(a):x(t) = (10cm)\cos \left[ {(\pi s^{ - 1} )t} \right] \hfill \\

(b):x(t) = (2.5cm)\sin \left[ {(5s^{ - 1} )t} \right] \hfill \\

\end{gathered}

[/tex]

Any help is appreciated, thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Write expressions for simple harmonic motion

**Physics Forums | Science Articles, Homework Help, Discussion**