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.
Maximum speed in SHM
Period from a T² graph
Vertical mass-spring system
Phase
Amplitude
Driven oscillation and resonance
Damping
Phase in SHM
SHM position as a cosine
v_max and a_max
Velocity and acceleration in SHM
Limits of the pendulum formula
Short answer 1. Define or explain: Simple harmonic motion
3 ptsShort answer 2. Define or explain: Velocity leads displacement by a quarter cycle
3 ptsShort answer 3. Define or explain: Period grows as the square root of mass
3 ptsShort answer 4. Define or explain: Slope of T² against m
3 ptsFree response
10 ptsA group of students is asked to determine the spring constant k of a spring using a mass hanger, a set of known masses, a stopwatch, and a meterstick. The students hang a mass m from the spring, displace it vertically, release it, and time the oscillations. Table 1 shows the period T measured for each mass. m (kg) 0.100 0.200 0.300 0.400 0.500 T (s) 0.63 0.89 1.09 1.26 1.40
A. Describe an experimental procedure for collecting the data in Table 1, including how the students should measure the period and one step that would reduce experimental uncertainty.
B. The period of a mass-spring oscillator is T = 2π√(m/k). Indicate what quantities the students should plot on the vertical and horizontal axes to produce a straight line whose slope can be used to determine k, and describe how the slope is related to k.
C(i). Calculate the values to be plotted on the vertical axis. C(ii). Describe the resulting graph, including the axis labels with units and the approximate positions of the plotted points. C(iii). Describe the best-fit line.
D. Using the best-fit line described in part C, calculate an experimental value for the spring constant k.