As per given figures, two springs of spring constants K and 2K are connected to mass m. If the period of oscillation in figure (a) is 3s, then the…
JEE Main 2022 — Physics Waves & Oscillations
2022integermedium
As per given figures, two springs of spring constants K and 2K are connected to mass m. If the period of oscillation in figure (a) is 3s, then the period of oscillation in figure (b) will be xs. The value of x is _____ .
Official previous-year question
Held on 26 Jul 2022 · Verified 6 Jul 2026.
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Solution
In figure (a), the springs are connected in series. Therefore,
Keq=K1+K2K1K2=K+2KK×2K=32K
Therefore, the time period
Ta=2πKeqm=2π32Km=2π2K3m
In figure (b), the springs are connected in parallel. Therefore,
Keq=K1+K2=3K
Therefore, the time period
Tb=2πKeqm=2π3Km
Now,
TbTa=29⇒Tb=32Ta=2s
Hence, x=2
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