Question

Q3. [21pts] Four people of total mass 300 kg get into a car. The car springs are compressed and the body of the car is lowered by 3 cm. Whilst driving, the car hits a bump on the road and oscillates vertically with a period of 0.75 s. a. Derive the value of the spring constant for the car suspension (the acceleration due to gravity can be taken as g = 9.8 ms). b. Derive the total mass of the car together with the occupants. Assume negligible damping. C. The damping on the suspension allows the oscillations to have decayed in 4 seconds. It is a known fact that the damping is proportional to -bv, where b is a constant and v is the velocity. Obtain a value for b and the quality factor Q.

Answer 1

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@ AF = kon - 300 x 9.8= kx 3x10-2 » K - 98000 N/m = 9.8x104 N/m = 98 kN/m assuming & = 0 TV - 2T 0.75 98x1000 M v 70.18385 = 98000 = M = 1396.33 kq M Total Mass = 1396.33kg abtes introduction of Dampes time period of oscillation increases as angulas frequency decreases. T X 2T Was Si-q? Wn 27 = 51&tx 27 Ta = I1 - 4 2 ) 4 = 01 75 * 16 256 => 1- + = 0.9822646 PO ME = = 0.9822646 T6 = 2298018 N-5/m Am