Question

The springs of a 1700 kg car compress 4.0 mm when its 64 kg driver gets into the driver's seat.

If the car goes over a bump, what will be the frequency of oscillations? Ignore damping.

Express your answer to two significant figures and include the appropriate units.

Answer 1

First, find the spring constant of the springs

Given that the springs of the car compress 4mm when its 64 kg driver gets into the driver's seat.

Use Hooke's Law

$F=kx$

$W=kx$

$mg=kx$

$\frac{mg}{x}=k$

$\frac{64kg*9.81m/s^{2}}{0.004m}=k$

$\frac{64*9.81}{0.004}=k$

${\color{Red} k=156960N/m}$

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Frequency, $f=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$

$f=\frac{1}{2\pi }\sqrt{\frac{k}{m_{car}+m_{driver}}}$

$f=\frac{1}{2\pi }\sqrt{\frac{156960N/m}{1700kg+64kg}}$

$f=\frac{1}{2\pi }\sqrt{\frac{156960}{1764}}$

ANSWER: ${\color{Red} f=1.5013Hz}$

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