~christina~

Gold Member

- 712

- 0

**[SOLVED] driving force- could someone tell me if I'm using the right method for probl**

**1. Homework Statement**

a 5.00kg mass attached to a spring of constant 150N/m. A driving force

[tex]F(t)= (120N)cos(\omega_d t) [/tex] is applied to the mass and the damping coefficient (b) is 6.00 N.s/m

a) what is the resonance frequency of this system?

b) what is the amplitude at resonance?

**3. The Attempt at a Solution**

First, I'm not sure what the dt is for in the equation..

**a) what is the resonance frequency of the system?**

[tex]F(t)= (120N)cos(\omega_d t) [/tex]

well....I'm not sure about the F(t) since they give it in cos but I assume that I can just write it with cos and it would be the same but not sure about that.. [and what is that d in the equation?]

if I'm right then it would be:

[tex]F(t)= (120N)sin(\omega_d t) [/tex] and

[tex]F_o= 12.0N [/tex]

resonance frequency is simply this I think:

[tex]\omega_o= \sqrt{\frac{k} {m} }[/tex]

and k is given as 150N/m

and the m is 0.500kg right?

**b) amplitude at resonance**

not sure about this..when something is at resonance what happens?

and what equation would I use to find this?

I thought that I would use this equation but

[tex]A= \frac{F_o/m} {\sqrt{(\omega^2-\omega_o^2)^2 + (\frac{b\omega} {m})^2}}[/tex]

would Fo be the result of pluging in 0 for the time in the driving force equation given?

and is [tex]\omega[/tex] found from this equation=> [tex]\omega= \sqrt{\omega_o^2-(\frac{b} {2m})^2} [/tex]

and then used to plug into the Amplitude of driven oscillator equation to find b?

like the title of the post says, I would really appreciate it if someone could tell

me if I'm doing the problem correctly.

Thank you