- #1
ViXXoR
- 6
- 0
Homework Statement
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]
Homework 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]
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
Last edited: