Discussion
Two springs of spring constant k1 and k2 are connected in parallel to a mass m. The effective time period of the system is
Answer: A
The period is \(2\pi\sqrt{\frac{m}{k_{1}+k_{2}}}\).
Springs in parallel stretch by the same amount, so their forces add and the effective spring constant is k1 + k2. The period of a mass-spring system is \(2\pi\sqrt{m/k}\), which gives option A.
Option B is the period for springs in series, where keff = \(\frac{k_{1}k_{2}}{k_{1}+k_{2}}\). Option C subtracts the constants, which no arrangement does, and option D inverts the series result.
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