A 1300 kg car is constructed on a frame that is is in turn supported by four springs. each spring has aspring constant of 2\cdot104\ N/m. Two passenge

Caelan

Caelan

Answered question

2021-01-28

A 1300 kg car is constructed on a frame that is is in turn supported by four springs. each spring has aspring constant of 2104Nm . Two passengers in the car have a combined mass of 160 kg. What is the frequency of free vibration of the car when it is driven ovr arough road? 
How long does it take the car to execute three complete oscillations?

Answer & Explanation

Ezra Herbert

Ezra Herbert

Skilled2021-01-29Added 99 answers

This is a Simple Harmonic Motion (SHM) problem. The mass ofthe car (1300 kg) sitting on the springs causes a displace menttowards the ground and this displacement can be considered the equilibrium position. When two passengers enter the vehicle, their total mass of 160 kg causes an extra displacement from the equilibrium position; we can also use this new position as an equilibrium position.
Mass of car+passangers=1300kg+160kg=1460kg
T=2πmk
Where...
T=Period
m=mass=1460kg
k=spring constant=2.0104 Nm
Hence...
T=2π1460kg2.0104 Nm=1.6976s1.7s
Frequency (F) is the inverse of T so...
F=11.7 s=0.5890...Hz0.6Hz
The period of an object under going SHM is defined as the time to complete one complete cycle. The time it takes to complete three full oscillations is:
31.7 s=5.1 s

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