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$A particle of mass m is attached to two identical springs of spring constant k each, arranged in a horizontal line. The particle is displaced by a small distance x from its equilibrium position along the line of the springs. What is the frequency of oscillation?$

A. $\frac{1}{2 π} \frac{k}{m}$
B. $\frac{1}{2 π} \frac{2 k}{m}$
C. $\frac{1}{2 π} \frac{k}{2 m}$
D. $\frac{1}{π} \frac{k}{m}$

Show correct answer & step-by-step solution

Correct answer: B — $\frac{1}{2 π} \frac{2 k}{m}$

Solution

$The restoring force on the mass is F = - k x - k x = - 2 k x .$
$The effective spring constant is k_{eff} = 2 k .$
$The angular frequency is ω = k_{eff} / m = 2 k / m .$
$The frequency is f = \frac{ω}{2 π} = \frac{1}{2 π} \frac{2 k}{m} .$
$Hence the answer is (B).$

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