Question

A mass of 5kg suspended from a spring with spring constant 400N/M. If the amplitude is 20cm, what is the maximum acceleration?

Answer 1

To find the maximum acceleration of the mass-spring system, we can use the equation for the maximum acceleration in simple harmonic motion (SHM), which is given by:

$a_{\text{max}}={\omega }^2\cdot A$

where: $a_{\text{max}}$ = maximum acceleration $\omega$ = angular frequency $A$ = amplitude of the motion

The angular frequency ($\omega$) of the mass-spring system can be calculated using the spring constant ($k$) and the mass ($m$) as follows:

$\omega =\sqrt{\frac{k}{m}}$

Given that the mass ($m$) is 5 kg and the spring constant ($k$) is 400 N/m, we can calculate the angular frequency ($\omega$):

ω=400 N/m5 kgomega = sqrt{frac{400 , ext{N/m}}{5 , ext{kg}}}ω=5kg<span class="pstrut" style="height: 3em;"