The natural frequency of a spring-mass system is originally 1 rad/s. T

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The natural frequency of a spring-mass system is originally 1 rad/s. The spring-mass system is connected to an inverted pendulum, with the spring attached to the midpoint of the pendulum, which has a length of 2l. Determine the mass ratio r (r = M/m) that restricts the natural frequency of the assembled system to less or equal to 2 rad/s. (Neglect the gravity, sin⁡θ ≈ θ, cos⁡θ ≈ 1)

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The natural frequency of a spring-mass system is originally $1 r a d / s$ . The spring-mass system is connected to an inverted pendulum, with the spring attached to the midpoint of the pendulum, which has a length of $2 l$ . Determine the mass ratio $r (r = M / m)$ that restricts the natural frequency of the assembled system to less or equal to $2 r a d / s$ . (Neglect the gravity, $\sin θ \approx θ, \cos θ \approx 1$ )