Ch- 14- sec8 Forced Oscillations; Resonance An 1150 kg automobile has springs wi

Question

Ch- 14- sec8 Forced Oscillations; Resonance An 1150 kg automobile has springs with k= 16,000N/m. one ofthe tires is not properly balanced; it has a little extra mass onone side compared to the other, causing the car to shake at certainspeeds. if the tire radius 42 cm, at what speed will the wheelshake most? - Thanks Ch- 14- sec8 Forced Oscillations; Resonance An 1150 kg automobile has springs with k= 16,000N/m. one ofthe tires is not properly balanced; it has a little extra mass onone side compared to the other, causing the car to shake at certainspeeds. if the tire radius 42 cm, at what speed will the wheelshake most? - Thanks

Explanation / Answer

Given : The car's speed can
be determined from the given tire radius.

Mass Supported By Each Of 4 Springs  
    m = (1/4) {Total Car Mass}
     = (1/4) (1150 kg)
     = 287.5 kg

Resonant Oscillation Period Of Each Spring = T =
     = 2**[ m/k ]
     = 2**[ (287.5)/(16000) ]
     = 0.84225 sec

Car Speed At Spring Resonance = v =
   = 2 (Tire Radius)/T   
     = 2 (0.42 m)/(0.84225 sec)
     = ---- m/sec
Solve it
I hope it helps you

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