Two springs of spring constants k_1 and k_2 a | vedclass

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(B) According to the figure, when the mass $m$ is displaced by a small distance $x$ to the right, the spring with constant $k_1$ is stretched by $x$ a

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$2 \pi \sqrt{\frac{m}{k_1+k_2}}$

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(B) According to the figure, when the mass $m$ is displaced by a small distance $x$ to the right, the spring with constant $k_1$ is stretched by $x$ and the spring with constant $k_2$ is compressed by $x$.The restoring force on the mass $m$ from the first spring is $F_1 = -k_1 x$.The restoring force on the mass $m$ from the second spring is $F_2 = -k_2 x$.The total restoring force is $F = F_1 + F_2 = -(k_1 + k_2)x$.This is in the form of $F = -k_{eq} x$, where the equivalent spring constant is $k_{eq} = k_1 + k_2$.The time period of oscillation for a mass-spring system is given by $T = 2 \pi \sqrt{\frac{m}{k_{eq}}}$.Substituting the value of $k_{eq}$, we get $T = 2 \pi \sqrt{\frac{m}{k_1 + k_2}}$.

Two springs of spring constants $k_1$ and $k_2$ are connected to a mass $m$ as shown in the figure. Under negligible friction, if the mass is displaced by a small amount $x$ from its equilibrium position and released, the period of oscillation is

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