Consider the double pendulum system connected via a spring, as shown below. (a) Assuming hinges to be frictionless, rods to be rigid and massless and both the angles to be small quantities, derive the applicable linear equations of motion. (Spring force is zero when 0 = 0). (1) (b) Next, create a block diagram by converting the above equations in Laplace domain and arrive at the transfer function between 0 and f by suitably reducing the block diagram. (3)