Respuesta :
Answer:
k = 9.6 x 10^5 N/m or 9.6 kN/m
Explanation:
First, we need to use the expression to calculate the spring constant which is:
w² = k/m
Solving for k:
k = w²*m
To get the angular velocity:
w = 2πf
The problem is giving the linear velocity of the car which is 5.7 m/s. With this we can calculate the frequency of the car:
f = V/x
f = 5.7 / 4.9 = 1.16 Hz
Now the angular velocity:
w = 2π*1.16
w = 7.29 rad/s
Finally, solving for k:
k = (7.29)² * 1800
k = 95,659.38 N/m
In two significant figures it'll ve 9.6 kN/m
Answer:
k=96.16 kN/m
Explanation:
Maximum amplitude is achieved, when the system operated in the resonance- frequency of the bumps is equal to the natural frequency of the spring-mass system.
Frequency of the bumps, as an input force:
f=V/d, where d- distance between the bumps and V- velocity of the resonance.
From the natural frequency of the spring- mass system, we can get:
[tex]f^{2}=\frac{1}{2\pi } \frac{k}{m}[/tex]
For the given problem, then the value of k, can be found as:
[tex]k=2\pi mf^{2}=2\pi m (\frac{V}{d}) ^{2} =96158 N/m[/tex]