Any help would be much appreciated. Thank you! We have found that many systems can be analyzed by using Newton's second law or Newton's second law for rotation and turning it into a differential equation. If the differential equation matches the one for simple harmonic motion, we can use the solutions for simple harmonic motion for the new system. Let's try this for a complicated system. Suppose we build a rigid pendulum with a ball of mass M on a length of rigid massless wire of length L (see the figure). Now suppose we attach a spring with a spring constant k to the pendulum at a distance h below its point of suspension, but we attach the spring in a way that only lets it move in the x-direction. We will only let this system experience small oscillations. Find the frequency of vibration of the system in terms of L, M, g, h, and k.

Views: 5,337 students