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
3.4 kgk = ?

A 3.4 kg mass on a spring makes 50 complete oscillations in 47 s. Find the spring stiffness k.

m = 3.4 kgN = 50t = 47 s
k = N/m
2.Easy
2.8 kgk14.5 cm

Hanging a 2.8 kg mass on a spring stretches it by 14.5 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 = 2.8 kgx = 14.5 cmg = 9.81 m/s²
T = s
3.Medium
L = 1.8 m

A simple pendulum has a length of 1.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.8 mg = 9.81 m/s²
T = s
4.Medium
L = 0.8 mT = 2.92 s

An astronaut on another planet finds that a simple pendulum 0.8 m long has a period of 2.92 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.8 mT = 2.92 s
g = m/s²
5.Hard
2.7 kgk = 400 N/mA = 11 cm

A 2.7 kg mass on a spring with k = 400 N/m is pulled 11 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.7 kgk = 400 N/mA = 11 cm
E = J
6.Hard
3 kgk = 20 N/mA = 2 cm

A 3 kg mass on a spring with k = 20 N/m is pulled 2 cm from equilibrium and released. Find its maximum speed vmax.

m = 3 kgk = 20 N/mA = 2 cm
vmax = m/s

Answer key

  1. 1. k = 151.9 N/m
  2. 2. T = 0.7639 s
  3. 3. T = 2.691 s
  4. 4. g = 3.704 m/s²
  5. 5. E = 2.42 J
  6. 6. vmax = 0.05164 m/s

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