Question

Show that the period of oscillation on a main helical spring is given by T=2π√{k/m}

Answer 1

Answer:

According to Newton's second law we have: $a=\dfrac{F}{m}=-\dfrac{k}{m}x;$

$a=-w^2x;$

Equating the two formulas for acceleration we obtain:

$-w^2x=-\dfrac{k}{m}x; w^2=\dfrac{k}{m}; w=\sqrt{\dfrac{k}{m}};$

$T=\dfrac{2\pi}{\omega}; T=2\pi\sqrt{\dfrac{m}{k}}.$