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)

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

)

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