A 2.00kg object attatched to a spring moves without friction and is driven by an external force given by
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= (Fo/m)/ sqrt(omega^2- omegao^2)^2 + (b*omega /m)^2
I think that..
omega= omegao
b= 0
so then
A= Fo/ 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
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
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.
Um I'm confused since that is the equation I got from my textbook so why is my book incorrect drwls?
To determine the period and amplitude of motion for the given system, we need to use the equations related to simple harmonic motion.
a) To find the period, we can use the equation T = 2π/ω, where ω is the angular frequency. In this case, the external force is given by F = (3.00N)sin(2πt), which can be rewritten as F = F₀sin(ωt), where F₀ = 3.00N and ω = 2π rad/s. Comparing this with the equation for the external force, we can see that ω is equal to the angular frequency of the system. Therefore, the period T is given by T = 2π/ω = 2π/(2π) = 1s.
b) To find the amplitude of motion, we can use the equation A = F₀/m/√(ω² - ω₀²)² + (bω/m)², where F₀ is the amplitude of the external force, m is the mass of the object, ω is the angular frequency of the system, ω₀ is the natural angular frequency of the system (determined by the spring constant), and b is the damping coefficient (in this case, it is 0 since there is no friction).
Since ω is equal to ω₀ and b = 0, the equation simplifies to A = F₀/m. Plugging in the values, we get A = 3.00N/2.00kg = 1.5m/s².
It seems that you made a mistake in converting the amplitude from meters to centimeters. The result you obtained, 1.5m/s², is in meters, not centimeters. To convert it to centimeters, you need to multiply by 100, so the correct amplitude is 1.5m/s² * 100cm/m = 150cm. Therefore, the amplitude of motion is 150cm or 1.5m.
To summarize:
a) The period T is 1 second.
b) The amplitude of motion A is 1.5m or 150cm.