Class 11 NEET Physics Oscillations Questions

The time period of a spring mass system as shown in figure 1 is given by T=2π√

m

k

, where k isthe spring constant.
∴ t1=2π√

m

k1

.....(i)
and t2=2π√

m

k2

....(ii)
Now, when they are connected in parallel as shown in figure 2(a), the system can be replaced by a single spring of spring constant, keff=k1+k2, as shown in figure 2(b)
[ since mg=k1x+k2x=keffx]
t0=2π√

m

keff

=2π√

m

(k1+k2)

....(iii)
From(i),

1

t12

=

1

4π2

×

k1

m

......(iv)
From(ii),

1

t22

=

1

4π2

×

k2

m

......(v)
From(iii), 1t02=

1

4π2

×

k1+k2

m

......(vi)
(iv) +(v)=

1

t12

+

1

t22

=

1

4π2m

(k1+k2)=

1

t02

∴t0−2=t1−2+t2−2