A 2.00kg object attatched to a spring moves without friction and is driven by an external force given by

Question

F= (3.00N)sin(2pi*t)

The force constant of the spring is 20N/m. Determine
a) period
b) amplitude of motion

a)T= 2pi/omega
T= 2pi/ 2pi= 1s

b)A= (F_o/m)/ sqrt(omega^2- omega_o^2)^2 + (b*omega /m)^2

I think that..
omega= omega_o
b= 0

so then

A= F_o/ m = 3.00N/2.00kg = 1.5 ???

My book states that a) is 1s but b) is 5.09cm which I can't seem to get.

Thanks
C

Answer 1

Um ...actually I figured that I got omega mixed up.

so basically I got the answer.

P.S. Thanks for helping me out with my other problems drwls

Answer 2

Your equation for A in terms of F/m is not correct. The lead term should be F/k, followed by a dimensionless amplification factor that depends upon the forcing frequency, natural frequency and damping. Since you are far from resonance, the damping term can be neglected or set equal to zero.

The equations you need can be found at
http://en.wikipedia.org/wiki/Vibration#Forced_vibration_with_damping, and in most introductory physics or mechanics texts.

Answer 3

Um I'm confused since that is the equation I got from my textbook so why is my book incorrect drwls?