Answer to Question #175118 in Physics for Joshua Musyoki

Question #175118

. A mass ,m, is hung on a helical spring of spring constant ,K, new tone 

and slightly displaced if it to oscillation has a period of 1 sec what will 

happen to the period when

i.) The a spring twice the length is used

ii.) Two identical springs in spring in series are use

iii.) The spring is made to vibrate in the moon where ‘g’ is a sixth that 

on Earth?

iv.) Two identical springs in spring in parallel are used


1
Expert's answer
2021-03-24T19:39:03-0400

The period of a mass oscillating on a spring is given by


T=2πmk.T=2\pi\sqrt{\frac{m}{k}}.

i.) A spring two times longer is used: nothing will change as the expression does not contain length.


ii.) Two identical springs in series are used: the spring constant will be


ks=k2,k_s=\frac{k}{2},Ts=2πmks=2π2mk=T2.T_s=2\pi\sqrt{\frac{m}{k_s}}=2\pi\sqrt{\frac{2m}{k}}=T\sqrt2.


The period will increase.


iii.) The spring is made to vibrate in the moon where ‘g’ is a sixth of that on Earth: nothing will change as there is no g in the equation.


iv.) Two identical springs in spring in parallel are used: the equivalent spring constant will be


kp=2k,Tp=2πmkp=2πm2k=T2.k_p=2k,\\ T_p=2\pi\sqrt{\frac{m}{k_p}}=2\pi\sqrt{\frac{m}{2k}}=\frac{T}{\sqrt2}.

The period will decrease.


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