It is given that the front natural frequency of a vehicle is 1.02 Hz and the rear natural frequency is 1.0 Hz The spring constants for front and rear tires is 1200 lb/in. Front and rear tires are loaded to 1000 lb and 760 lb each, respectively. Find the front and rear suspension spring constants that will provide these frequencies.
To find the front and rear suspension spring constants that will provide the given frequencies, we can use the equation for the natural frequency of a mass-spring system:
ω = sqrt(k / m)
where
ω is the angular frequency (2π is the spring constant, and
m is the mass.
We can use this equation for both the front and rear tires to determine their respective spring constants.
For the front tires:
Given:
Angular frequency ω(front) = 2πf(front) = 2π * 1.02 Hz
Load on front tires m(front) = 1000 lb
Rearranging the equation, we have:
k(front) = (ω(front))^2 * m(front)
k(front) = (2π * 1.02)^2 * 1000
Now, let's calculate k(front):
k(front) = (2π * 1.02)^2 * 1000
k(front) ≈ 6513.57 lb/in
Therefore, the front suspension spring constant is approximately 6513.57 lb/in.
Now, let's calculate the rear suspension spring constant:
Given:
Angular frequency ω(rear) = 2πf(rear) = 2π * 1.0 Hz
Load on rear tires m(rear) = 760 lb
Rearranging the equation, we have:
k(rear) = (ω(rear))^2 * m(rear)
k(rear) = (2π * 1.0)^2 * 760
Now, let's calculate k(rear):
k(rear) = (2π * 1.0)^2 * 760
k(rear) ≈ 4790.58 lb/in
Therefore, the rear suspension spring constant is approximately 4790.58 lb/in.
To summarize:
Front suspension spring constant ≈ 6513.57 lb/in
Rear suspension spring constant ≈ 4790.58 lb/in