An automobile can be considered to be mounted on four identical springs as far a

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 1700 kg and the weight is evenly distributed over the springs? _____ N/m (b) What will be the vibration frequency if five passengers, averaging 66.0 kg each, ride in the car with an even distribution of mass? _____ Hz

Explanation / Answer

T = 2(m/k)
k = 4²m / T²
The load on a spring =1700/4 =425kg
T = 1 / 2 = 0.5s

k = 4² x 425 / (0.5s)² = 6.71*10^4 N/m

b) New load on a spring = (1700 + [5 x66]) / 4 = 507.5 kg

T = 2(M/k) .. .. 2(507.5 / 6.71*10^4) = .546 s

Frequency .. F = 1/ T = 1/ 0.546s .F = 1.83 Hz

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