A block of mass $m$ on a smooth horizontal surface is attached to two walls by springs of constant $k_1$ and $k_2$ on opposite sides. Time period of small oscillations:
A$2\pi\sqrt{m/k_1}$
B$2\pi\sqrt{m/(k_1 + k_2)}$
C$2\pi\sqrt{m(k_1+k_2)/(k_1 k_2)}$
D$2\pi\sqrt{m k_1 k_2/(k_1+k_2)}$
Answer & Solution
Correct answer: B. $2\pi\sqrt{m/(k_1 + k_2)}$
When block moves by $x$ to one side, one spring is compressed ($-k_1 x$), other is stretched (also $-k_2 x$). Both push back. Net restoring force = $-(k_1+k_2)x$. So springs act in **parallel** (despite being on opposite sides). $T = 2\pi\sqrt{m/(k_1+k_2)}$.
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