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
0.2 kgk = ?7.5 cm

Hanging a 0.2 kg mass on a spring stretches it by 7.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.2 kgx = 7.5 cmg = 9.81 m/s²
k = N/m
2.Easy
3 kgk = ?13 cm

Hanging a 3 kg mass on a spring stretches it by 13 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 3 kgx = 13 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 1.5 mT = 1.55 s

An astronaut on another planet finds that a simple pendulum 1.5 m long has a period of 1.55 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.5 mT = 1.55 s
g = m/s²
4.Medium
L = 0.7 mT = 2.73 s

An astronaut on another planet finds that a simple pendulum 0.7 m long has a period of 2.73 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.7 mT = 2.73 s
g = m/s²
5.Hard
1.4 kgk = 130 N/mA = 12 cm

A 1.4 kg mass on a spring with k = 130 N/m is pulled 12 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.4 kgk = 130 N/mA = 12 cm
E = J
6.Hard
1.1 kgk = 460 N/mA = 16 cm

A 1.1 kg mass on a spring with k = 460 N/m is pulled 16 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.1 kgk = 460 N/mA = 16 cm
E = J

Answer key

  1. 1. k = 26.16 N/m
  2. 2. k = 226.4 N/m
  3. 3. g = 24.65 m/s²
  4. 4. g = 3.708 m/s²
  5. 5. E = 0.936 J
  6. 6. E = 5.888 J

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