Answer:
The maximum acceleration amplitude is 40.28 g.s.
Explanation:
Given that,
Full scale suspension = 25 mm
Frequency = 20 Hz
We need to calculate the maximum frequency
Using formula of maximum frequency
[tex]f=\dfrac{\omega}{2\pi}[/tex]
[tex]\omega=f\times2\pi[/tex]
Put the value into the formula
[tex]\omega=20\times2\pi[/tex]
[tex]\omega=40\pi\ rad/s[/tex]
We need to calculate the maximum acceleration amplitude
Using restoring force
[tex]F= -kx[/tex]
[tex]ma=-kx[/tex]
[tex]a=\dfrac{-kx}{m}[/tex]
[tex]a=-\omega^2 x[/tex]
[tex]|a|=\omega^2 x[/tex]
Using equation of S.H.M
[tex]x=A\sin\omega t[/tex]
On differentiating
[tex]\dfrac{dx}{dt}=A\omega\cos\omega t[/tex]
On differentiating again
[tex]\dfrac{d^2x}{dt^2}=-\omega^2A\sin\omega t[/tex]
[tex]a=-\omega^2A\sin\omega t[/tex]
Maximum acceleration =ω²A
Which is at the maximum amplitude
[tex]a =\omega^2 A[/tex]
[tex]a=(40\pi)^2\times25\times10^{-3}[/tex]
[tex]a=394.78\ m/s^2[/tex]
[tex]a=\dfrac{394.78}{g}[/tex]
[tex]a=40.28\ g.s[/tex]
Hence, The maximum acceleration amplitude is 40.28 g.s.
