Answer:
[tex]T= 2\pi\times sqrt(m/(k1+k2))[/tex]
Explanation:
When the block is displaced by x units
F= spring force
two springs are connected parallel
[tex]F =-k_1x - k_2x[/tex]
Writing Newtons second law, F = ma
[tex]-k_1x - k_2x =ma[/tex]
[tex]-k_1x - k_2x = mx''[/tex]
a= x" ( differentiating x w.r.t time twice)
[tex]x''+(k_1/m + k_2/m) x=0[/tex]
this the standard form of equation of oscillation spring mass system
This is the differential equation, x'' means that double differentiation of x , i.e, x'' is acceleration
since, Period [tex]T=2\pi\sqrt{\frac{m}{K_{eq.}} }[/tex]
therefore,
[tex]T= 2\pi\times sqrt(m/(k1+k2))[/tex]
