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### 1.2.5 Example

The graphs show how the variation with time of the velocity, v and the acceleration, a of a body when it is oscillating with simple harmonic motion.

(a) Determine the period, T.

(b) Sketch the variation with time of the displacement, x, of the oscillating body

[ 2.09 s, x = 2 sin( 3t )]

### 1.2.5.1 Solution:

a) maximum velocity , v_{0} = x_{0}ω = 6 m/s

maximum acceleration a_{0} = x_{0}ω^{2} = 18 m/s^{2}

thus dividing the 2 equations, we get ω = 3 rad/s

therefore since $\omega =\genfrac{}{}{0.1ex}{}{2\pi}{T}$

$3=\genfrac{}{}{0.1ex}{}{2\pi}{T}$

$T=\genfrac{}{}{0.1ex}{}{2\pi}{3}$

$T=2.09s$

$T=\genfrac{}{}{0.1ex}{}{2\pi}{3}$

$T=2.09s$

b) since maximum velocity , v

_{0}= x_{0}ω = 6 m/s and we now know ω = 3 rad/s earlierx

x

_{0}(3) = 6x

_{0}= 2 musing the model to test check out your answer!

### 1.2.5.2 Model:

### For Teachers

### Translations

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