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.
Amplitude
Why T is independent of amplitude
Why acceleration is opposite displacement
Squaring a period to linearize it
Driven oscillation and resonance
Period of a mass on a spring
Period and frequency
Where speed is maximum
Period from a T² graph
Energy in SHM scales with amplitude squared
Velocity and acceleration in SHM
v_max and a_max
Short answer 1. Define or explain: SHM position as a cosine
3 ptsShort answer 2. Define or explain: Limits of the pendulum formula
3 ptsShort answer 3. Define or explain: Acceleration is the displacement graph inverted
3 ptsShort answer 4. Define or explain: Period of a spring on a different planet
3 ptsFree response
8 ptsTwo identical springs, each of spring constant k, are used to build two oscillators on a horizontal frictionless surface. Oscillator 1 consists of a block of mass m attached to one spring. Oscillator 2 consists of a block of mass 2m attached to the other spring. Each block is pulled the same distance A from equilibrium and released from rest.
A. Indicate whether the period of oscillator 2 is greater than, less than, or equal to the period of oscillator 1. Justify your answer using qualitative reasoning beyond referencing equations.
B. Starting from Newton’s second law or from conservation of energy, derive an expression for the maximum speed of a block of mass m attached to a spring of constant k and released from rest at displacement A.
C. Justify how your derived expression in part B is or is not consistent with the comparison of maximum speeds of the two oscillators.