Answer to Question #175118 in Physics for Joshua Musyoki

Question

. 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

Answer 1

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

$$T=2\pi\sqrt{\frac{m}{k}}.$$

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

$$k_s=\frac{k}{2},$$ $$T_s=2\pi\sqrt{\frac{m}{k_s}}=2\pi\sqrt{\frac{2m}{k}}=T\sqrt2.$$

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

$$k_p=2k,\\ T_p=2\pi\sqrt{\frac{m}{k_p}}=2\pi\sqrt{\frac{m}{2k}}=\frac{T}{\sqrt2}.$$

The period will decrease.