Question

A student measures the maximum speed of a block undergoing simple harmonic oscillations of amplitude A on the end of a single ideal spring with spring constant k. The single spring is then replaced with 3 identical springs (in series) with the same spring constant k. If the same block undergoes SHM with the same amplitude before, by what factor does the maximum speed change?

Answer 1

Answer:

Explanation:

Given

Amplitude of oscillation is A

spring constant k

suppose m is the mass of block so its natural frequency of oscillation is given by

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

$v_{max}=A\omega =A\cdot \sqrt{\frac{k}{m}}$

When three identical springs is connected in series

$k_{effectice}=\frac{k}{3}$

Natural Frequency becomes

$\omega _n=\sqrt{\frac{k}{3m}}$

Thus maximum speed with Amplitude A is

$v'_{max}=A\cdot \sqrt{\frac{k}{3m}}$

so by a factor of $\frac{1}{\sqrt{3}}$ maximum velocity is changed