(Solved): B-3-4. Consider the spring-loaded pendulum system shown in Figure 3-33. A ssume that the spring for ...

B-3-4. Consider the spring-loaded pendulum system shown in Figure 3-33. A ssume that the spring force_acting on the pendulum is zero when the pendulum is vertical, or \( \theta=0 \). Assume also that the friction involved is negligible and the angle of oscillation \( \theta \) is small. Obtain a mathematical model of the system. Figure 3-33 Spring-loaded pendulum system. B-3-4 Assume the angle is small, so the point where the springs are attached can be viewed as moving horizontally by theta*a. Obtain an equation in theta and find a transfer function for the system assuming the input is a torque applied to the rod, and the output is theta You may need to linearize some terms for theta near zero \( \sin \) (theta) is about theta, and \( \cos ( \) theta) is about \( 1 . \)