Oscillations unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Vertical mass–spring equilibrium
Defining condition for SHM
Maximum speed in SHM
Simple pendulum period
Effect of amplitude on a real pendulum
Maximum acceleration in SHM
Deriving the pendulum period
Physical pendulum
Where kinetic and potential energy peak
Underdamped, critically damped, overdamped
Pendulum period independent of mass
Average energy over a cycle
Short answer 1. Define or explain: Energy decay in a damped oscillator
3 ptsShort answer 2. Define or explain: Angular frequency of a mass–spring system
3 ptsShort answer 3. Define or explain: Phase relationships
3 ptsShort answer 4. Define or explain: Period independent of amplitude
3 ptsFree response
12 ptsTRANSLATION BETWEEN REPRESENTATIONS (Question 2, 12 points). In Scenario 1, a system of two springs (A and B) and a block of mass m rests on a frictionless horizontal surface. Each spring connects a fixed wall to the block: Spring A has spring constant k and Spring B has spring constant 2k, and each is at its relaxed length when the block is at x = 0. The block is moved to x = x1 and held at rest (Figures 1–2). Figure 3 provides an energy bar chart for UA (Spring A's elastic potential energy), UB (Spring B's), and Kblock. For C: in Scenario 1 the block oscillates with period T (Figure 4 shows x versus t). In Scenario 2 the block-springs system is placed on a surface with friction, again pulled to x1 and released; it oscillates with the same period, completing several oscillations before stopping (Figure 5 provides axes for kinetic energy K versus t). For D: in Scenario 3 a new block of larger mass replaces the original on the Scenario 2 surface (same coefficient of kinetic friction), is pulled to x1, and released; its K versus t is plotted.
A. Describe the energy bar chart at x = x1: the bars for UA, UB, and Kblock, with heights proportional to the energies (zero energies drawn as a distinct line at zero).
B. The block is released from rest at x = x1. Derive an expression for the speed v of the block as it passes through x = x1/2, in terms of m, k, x1, and physical constants, as appropriate.
C. Describe the graph of the kinetic energy K of the block as a function of t for Scenario 2.
D. Describe how one feature of the K-versus-t graph in Scenario 3 would differ from your Scenario 2 graph, and briefly justify your answer.