Question

A bike racing team is picking an accelerometer to measure the vertical acceleration of a front suspension. They know that the full-scale suspension travel is ±25 mm and the maximum frequency of motion is 20 Hz. Assuming that this acceleration can be modeled as a sinusoid, what is the maximum acceleration amplitude that they can expect to measure? Give your answer in g’s.

Answer 1

The maximum acceleration amplitude is 40.28 g.s.

Step-by-step explanation:

Given that,

Full scale suspension = 25 mm

Frequency = 20 Hz

We need to calculate the maximum frequency

Using formula of maximum frequency

`f=(\omega)/(2\pi)`

`\omega=f*2\pi`

Put the value into the formula

`\omega=20*2\pi`

`\omega=40\pi\ rad/s`

We need to calculate the maximum acceleration amplitude

Using restoring force

`F= -kx`

`ma=-kx`

`a=(-kx)/(m)`

`a=-\omega^2 x`

`|a|=\omega^2 x`

Using equation of S.H.M

`x=A\sin\omega t`

On differentiating

`(dx)/(dt)=A\omega\cos\omega t`

On differentiating again

`(d^2x)/(dt^2)=-\omega^2A\sin\omega t`

`a=-\omega^2A\sin\omega t`

Maximum acceleration =ω²A

Which is at the maximum amplitude

`a =\omega^2 A`

`a=(40\pi)^2*25*10^(-3)`

`a=394.78\ m/s^2`

`a=(394.78)/(g)`

`a=40.28\ g.s`

Hence, The maximum acceleration amplitude is 40.28 g.s.