Question

Part A

Your friend helps you place a 105 kg sofa in the back of a 2200 kg truck. Your keen vision tells you that the truck sinks 3.75 cm on its springs when you place the sofa. With what frequency (in Hz) will the truck and the sofa oscillate on the springs?

Answer 1

First, find the spring constant of the springs

Given that the truck sinks 0.0375m when a 105kg sofa is placed on it

Use Hooke's Law

$F=kx$

$W=kx$

$mg=kx$​​​​​​

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

$\frac{105kg*9.81m/s^{2}}{0.0375m}=k$

$\frac{105*9.81}{0.0375}=k$

${\color{Red} k=27468N/m}$

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

$f=\frac{1}{2\pi }\sqrt{\frac{k}{m_{truck}+m_{sofa}}}$

$f=\frac{1}{2\pi }\sqrt{\frac{27468N/m}{2200kg+105kg}}$

$f=\frac{1}{2\pi }\sqrt{\frac{27468}{2200+105}}$

ANSWER: ${\color{Red} f=0.55Hz}$

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