Four passengers with combined mass 250 kg compress the springs of a car with worn out shock absorbers by 4.00cm when they enter it. Model the care and passengers as a single body on a single ideal spring. If the loaded has a period of vibration of 1.08 s, what is the period of vibration of the empty car?

The time period of the empty car will be "1.00 s".

Explanation:

The given values in the question will be:

Mass,

m = 250 kg

Loaded car's time period will be:

T = 1.08 s

Shock absorbers compression,

x = 4 cm

or,

  = 0.04 m

Now,

Weight of passengers will be:

⇒  

The spring constant of shock absorbers will be:

⇒  

As we know,

Time period,

On substituting the values, we get

                            (Total mass of car as well as its passengers)

Now,

The mass of the empty car will be:

⇒  

hence,

The time period of empty car will be:

⇒  

or,

car a and b are moving in opposite directions

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