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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 :

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

[tex]\omega _n=\sqrt{\frac{k}{m}}[/tex]

[tex]v_{max}=A\omega =A\cdot \sqrt{\frac{k}{m}}[/tex]

When three identical springs is connected in series

[tex]k_{effectice}=\frac{k}{3}[/tex]

Natural Frequency becomes

[tex]\omega _n=\sqrt{\frac{k}{3m}}[/tex]

Thus maximum speed with Amplitude A is

[tex]v'_{max}=A\cdot \sqrt{\frac{k}{3m}}[/tex]

so by a factor of [tex]\frac{1}{\sqrt{3}}[/tex] maximum velocity is changed      

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