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

Damping is negligible for a 0.155 kg object hanging from a light 6.30 N/m spring. A sinusoidal force with an amplitutde of 1.70 N drives the system. At what frequency will the force make the object vibrate with an amplitude of 0.440 m?

So:

[tex]m=0.155kg[/tex]

[tex]k=6.30N/m[/tex]

[tex]F=1.70N[/tex]

[tex]A=0.440m[/tex]

2. Relevant equations

So a given equation is:

[tex]A = \frac{\frac{F}{m}}{\sqrt{\beta^2 - \beta o^2 + (\frac{b\beta}{m})^2}}[/tex]

Also:

[tex]\beta o = \sqrt{\frac{k}{m}}[/tex] so [tex]\beta o = \sqrt{\frac{6.30}{0.155}} = 40.6452 rad/s[/tex]

And:

[tex]f = \frac{\beta}{2\pi}[/tex]

3. The attempt at a solution

Damping is negligible so [tex](\frac{b\beta}{m})^2}} = 0[/tex]

Rearranging the first equation for [tex]\beta[/tex]:

[tex]\beta = \sqrt{\frac{(\frac{F}{m})^2}{A^2} + \beta o^2[/tex]

Plug in all the values:

[tex]\beta = \sqrt{\frac{(\frac{1.70}{0.155})^2}{0.440^2} + 40.6452^2}

= 47.6799 rad/s[/tex]

Now using the formula for frequency:

[tex]f = \frac{\beta}{2\pi}

= \frac{47.6799}{2\pi}

= 7.5885 Hz[/tex]

It seems my answer is wrong, and I cannot find out where I am going wrong. Any advice would be greatly appreciated.

Thanks

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# Finding a frequency to create a given amplitude in a spring

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