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
4.6 kgk = 360 N/m

A 4.6 kg mass on a spring with stiffness 360 N/m oscillates on a frictionless surface. Find the period T.

m = 4.6 kgk = 360 N/m
T = s
2.Easy
3 kgk = ?3.5 cm

Hanging a 3 kg mass on a spring stretches it by 3.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 3 kgx = 3.5 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 2.6 m

A simple pendulum has a length of 2.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.6 mg = 9.81 m/s²
T = s
4.Medium
L = 1.8 mT = 2.83 s

An astronaut on another planet finds that a simple pendulum 1.8 m long has a period of 2.83 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.8 mT = 2.83 s
g = m/s²
5.Hard
2.9 kgk = 320 N/m

A 2.9 kg mass is attached to the lower end of an unstretched vertical spring with k = 320 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2.9 kgk = 320 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
3.5 kgk = 1900 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 = 1900 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 200 m/sM = 3.5 kgk = 1900 N/m
A = cm

Answer key

  1. 1. T = 0.7102 s
  2. 2. k = 840.9 N/m
  3. 3. T = 3.235 s
  4. 4. g = 8.873 m/s²
  5. 5. vmax = 0.9339 m/s
  6. 6. A = 4.891 cm

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