Two springs are connected in parallel to a 1.0-kg mass. If the spring constants are k₁ = 15.0 N/m and k₂ = 10.0 N/m, the period of the motion is A) 1.26 s. B) 2.56 s. C) 2.81 s. D) 3.61 s.

Question

Quizplus · Accepted Answer

The period of motion for a mass attached to springs in parallel is given by $T = 2\pi\sqrt{\frac{m}{k_{\text{eff}}}}$, where $k_{\text{eff}} = k_1 + k_2$ for springs in parallel. Here, $k_{\text{eff}} = 15.0\, \text{N/m} + 10.0\, \text{N/m} = 25.0\, \text{N/m}$. Substituting $m = 1.0\, \text{kg}$ and $k_{\text{eff}} = 25.0\, \text{N/m}$ into the formula gives $T = 2\pi\sqrt{\frac{1.0}{25.0}} \approx 1.26\, \text{s}$.

Two Springs Are Connected in Parallel to a 1