Question

An automobile can be considered to be mounted on four identical springs as far as vertical oscillations are concerned. The springs of a certain car are adjusted so that the oscillations have a frequency of 2 Hz.
(a) What is the spring constant of each spring if the mass of the car is 1250 kg and the weight is evenly distributed over the springs?

My Work:

ω = 2πf = 2π(2Hz) = 12.56637061 rad/s; k = mω² = [1250kg(12.56637061 rad/s)^2]/4 = 49348.02197 N/m (Note: I divided by four because we only wanted the spring constant of one spring)

My Answer:

49348.02197 N/m

(b) What will be the vibration frequency if five passengers, averaging 76.0 kg each, ride in the car with an even distribution of mass?

My Work:

mass of car = 1250kg; mass per person = 76.0kg >> 76.0*5 = 380kg >> Total mass with passengers = 1250kg + 380kg = 1630kg; ω = √(k/m) = √[(49348.02197N/m)/(1630kg)] = 5.502259545 Hz (tried it again) took 1630kg/4 = 407.5kg >> ω = √[(49348.02197N/m)/(407.5kg)] = 11.00451909 Hz

My Answer:

11.00451909 Hz

I''m confused on where my mistake is on this problem. Please help.

Answer 1

PP10606-11: An automobile can be considered to be mounted on four identical springs as far as vertical oscillations are concerned. The springs of a cestain car are adjusted so that the oscilations have a frequency of 3.00 Hz. (a) What is the spring constant of each spring if the mass of the car is 1450 kg and the mass is evenly distributed over the springs? (b) What will be the osclation frequency if five passengers, averaging 73.0 kg each, ride in the car? (Again, consider an even distribution of mass.) Spting 2003

Answer 2

)-( 125 ) (2π *2)2-4935 * 104N/m

First ans is right.

b)

]

4.9358 10 4 ' 11,0 l rad/s =

1101 = 1.75Hz

You did not convert to Hz at the end.

Answer 3

Well, there is a formula for the resonant frequency of a mechanical system:
f = 1/(2.pi) . SQRT( k/M )
where k is the spring constant and M is the mass.

a) In this case, f = 2.5, M = 1455. Put these in the equation to get k. Since k is being provided by 4 springs, the spring constant of each spring will be k/4

b) Now the mass has increased by 5 x 67 = 335kg. The total M = 1455 + 335 = 1790. Use the equation with this new M to get the new f.

BTW the question states that the mass and springs and passengers are evenly distributed. This is important because if they were not then you would get rolling and pitching of the car and the oscillation would be in multiple dimensions.