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Worksheet: The Spring Problem

Q1:

A spring is fixed at one end and hangs vertically. Its lower end is pulled 19 cm down from its equilibrium position and released. It performs 13 oscillations every second and, after 4 seconds, the amplitude decreases to 14 cm. Find a function that models , the displacement of the end of the spring from its equilibrium position, in terms of , the time in seconds after it is released.

  • A
  • B
  • C
  • D
  • E

Q2:

A spring is fixed at one end and hangs vertically. Its lower end is pulled 32 cm down from its equilibrium position and released. It performs 8 oscillations every second, and the amplitude of the oscillations decreases by each second. How long does it take for the amplitude of its oscillations to decrease to 0.1 cm? Give your answer to three decimal places.

  • A6.315 seconds
  • B8.315 seconds
  • C8.322 seconds
  • D9.944 seconds
  • E9.944 seconds

Q3:

A spring is fixed at one end and hangs vertically. Its lower end is pulled 7 cm down from its equilibrium position and released. It performs 20 oscillations every second, and the amplitude of the oscillations decreases by each second. Find a function that models , the displacement of the end of the spring from its equilibrium position, in terms of , the time in seconds after it is released.

  • A
  • B
  • C
  • D
  • E

Q4:

A spring is fixed at one end and hangs vertically. Its lower end is pulled 17 cm down from its equilibrium position and released. It performs 14 oscillations every second, and, after 3 seconds, the amplitude of the oscillations is 13 cm. Find a function that models , the displacement of the end of the spring from its equilibrium position, in terms of , the time in seconds after it was released.

  • A
  • B
  • C
  • D
  • E