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A car servicing station has 3 stalls where servicing can be offered simultaneously. The cars wait in such a way that when a stall becomes vacant, the car at the head of the line pulls up to it. The station can accommodate at most four cars waiting (seven in station) at one time. The arrival patterns are Poisson with a mean of one car per minute during the peak hours. The service time is exponential with mean 6 minutes. Find the average number of cars in the service station during peak hours, the average waiting time and the average number of cars per hour that cannot enter the station because of full capacity
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A vibrating system of 2𝑔 mass is displaced from its mean position. If the restoring force acting on
the mass is 5 𝑑𝑦𝑛𝑒 /𝑐𝑚 and damping factor is 1𝑑𝑦𝑛𝑒/𝑐𝑚 𝑠
−1
. Check if the motion is aperiodic or
oscillatory. If oscillatory calculate the time period of oscillation. Calculate the 𝑄 value and
logarithmic decrement of the system.
