A particle at the end of a spring executes simple harmonic motion with a period t1, while the corresponding period for another spring is t1 If theperiod of oscillation with the two springs in series is T , then

Here, t1=2πmk1  or  t12=4π2mk1  and t2=2πmk2  or  t22=4π2mk2 âˆ´ t12+t22=4π2m1k1+1k3 When the springs are connected h seri6s, then 1k=1k1+1k2  Now T=2πmk =2πm1k1+1k2 or T2=4π2m1k1+1k2 T2=4π2m1k1+1k2 Fmm eqs. [1) atrd (2), we ge T2=t12+t22