Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
0.8 kgk12.5 cm

Hanging a 0.8 kg mass on a spring stretches it by 12.5 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 0.8 kgx = 12.5 cmg = 9.81 m/s²
T = s
2.Easy
3.9 kgk = 40 N/m

A 3.9 kg mass on a spring with stiffness 40 N/m oscillates on a frictionless surface. Find the period T.

m = 3.9 kgk = 40 N/m
T = s
3.Medium
L = 1.7 mT = 6.44 s

An astronaut on another planet finds that a simple pendulum 1.7 m long has a period of 6.44 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.7 mT = 6.44 s
g = m/s²
4.Medium
L = 0.4 m

A simple pendulum has a length of 0.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.4 mg = 9.81 m/s²
T = s
5.Hard
3.5 kgk = 700 N/m200 m/s

A 20 g bullet moving at 200 m/s hits and stays in a 3.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 700 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 200 m/sM = 3.5 kgk = 700 N/m
A = cm
6.Hard
2 kgk = 500 N/m300 m/s

A 5 g bullet moving at 300 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 500 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 5 gv = 300 m/sM = 2 kgk = 500 N/m
A = cm

Answer key

  1. 1. T = 0.7093 s
  2. 2. T = 1.962 s
  3. 3. g = 1.618 m/s²
  4. 4. T = 1.269 s
  5. 5. A = 8.058 cm
  6. 6. A = 4.737 cm

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