Part 3: The Period of a Mass on Two Springs in Parallel Conguration 1. We will use two springs to support the mass oriented in parallel (see photo below). The medium and long springs were used. 2. When springs are in combination, together in one system, they act as if you had one spring with a different spring constant. We call this combined constant the "effective spring constant" keff. That means that these two springs together cause a vibration just like a single spring which had this keg as its spring constant The period of the system is now that calculated by the same formula above, but with k equaling this effective spring constant. 3. So we need to come up with an expression for keff which will allow us to use the k's from part 1 to calculate the keff. We will work algebraically with the two k's. Don't nd keg as in part 1. 4. Finding the formula for keff: keff for parts 3, 4 and 5 will be an algebraic combination of the individual k's. We need to develop an equation in the form Ftotal = keff Ax. In this rst situation (parallel springs), the sum of the forces by the two individual springs equal the total upward force acting on the mass, so we start with Fm : F1 ~l~ F2. Also Ax is the same for both of these springs, so it can be factored out and cancelled. 5. Therefore: keffAm 2 191 Am l kgAx and keff 2 k1 l [:2 This is ourformula. 6. The two springs are the medium and the long springs. The mass is 100g + 50 g + the hanger. Use the formula to calculate keff and then use that to predict the period of this system as you did in part 2. 7. Find the experimental period using your stopwatch. 8. Find the percent difference between prediction and experimental values. Part 3: Mass on Two Springs in Parallel Spring 1 Spring 2 m k. k; ken T (pred) t (10 T % Diff ID ID cycles} (exp)