An automobile can be considered to be mounted on four identical
springs as far as vertical oscillations are concerned. The springs
of a certain car are adjusted so that the oscillations have a
frequency of 2 Hz.
(a) What is the spring constant of each spring if the mass of the
car is 1250 kg and the weight is evenly distributed over the
springs?
My Work:
ω = 2πf = 2π(2Hz) = 12.56637061 rad/s; k = mω2 =
[1250kg(12.56637061 rad/s)^2]/4 = 49348.02197 N/m (Note: I divided
by four because we only wanted the spring constant of one
spring)
My Answer:
49348.02197 N/m
(b) What will be the vibration frequency if five passengers,
averaging 76.0 kg each, ride in the car with an even distribution
of mass?
My Work:
mass of car = 1250kg; mass per person = 76.0kg >> 76.0*5 = 380kg >> Total mass with passengers = 1250kg + 380kg = 1630kg; ω = √(k/m) = √[(49348.02197N/m)/(1630kg)] = 5.502259545 Hz (tried it again) took 1630kg/4 = 407.5kg >> ω = √[(49348.02197N/m)/(407.5kg)] = 11.00451909 Hz
My Answer:
11.00451909 Hz
I''m confused on where my mistake is on this problem. Please help.
First ans is right.
b)
]
You did not convert to Hz at the end.
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