Question

0 w k mg k 1. Consider the spring loaded pendulum shown above. Assume that the spring force acting on the pendulum is zero when the pendulum is vertical ($\theta = 0$). Assume that $\theta$ is small, so $\sin\theta \approx \theta$ and $\cos\theta \approx 1$. Also note that for small $\theta$, the spring force is approximately horizontal. Obtain the state variable representation of the system if $x_1$ is the angular position and $x_2$ is the angular velocity of the pendulum.

          0
w
k
mg
k
1. Consider the spring loaded pendulum shown above. Assume that the spring force acting on the
pendulum is zero when the pendulum is vertical ($\theta = 0$). Assume that $\theta$ is small, so $\sin\theta \approx \theta$ and
$\cos\theta \approx 1$. Also note that for small $\theta$, the spring force is approximately horizontal. Obtain the state
variable representation of the system if $x_1$ is the angular position and $x_2$ is the angular velocity of the
pendulum.

0
w
k
mg
k
1. Consider the spring loaded pendulum shown above. Assume that the spring force acting on the
pendulum is zero when the pendulum is vertical (θ = 0). Assume that θ is small, so sinθ≈θ and
cosθ≈ 1. Also note that for small θ, the spring force is approximately horizontal. Obtain the state
variable representation of the system if x1 is the angular position and x2 is the angular velocity of the
pendulum.

Added by Thomas R.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Thanks for your feedback!

Pendulum. Variable representation of the system if Î¸ is the angular position and Ï‰ is the angular velocity of the cosÎ¸. Also note that for small Î¸, the spring force is approximately horizontal. Obtain the state WMM.