Question

Your friend helps you place a 105 kg sofa in the back of a 2600 kg truck. Your keen vision tells you that the truck sinks 3.5 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

To develop this problem it is necessary to apply the concepts related to frequency from Hooke's law.

By Hooke's law we know that the Force is defined as

$F = k\Delta x$

Where,

k = Spring constant

$\Delta x =$Displacement

at the same time Force can be defined by Newton's second law as,

F = mg

Where,

m = mass

g = gravity

Equating we have

$mg = k \Delta x$

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

$k = \frac{105(9.8)}{3.5*10^{-2}}$

$k = 29400N/m$

Frequency and oscillation can be defined as

$f = \frac{1}{2\pi} \sqrt{\frac{k}{m+M}}$

Then replacing,

$f = \frac{1}{2\pi} \sqrt{\frac{29400}{105+2600}}$

$f = 0.5246Hz$