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
1.2 kgk13 cm

Hanging a 1.2 kg mass on a spring stretches it by 13 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 = 1.2 kgx = 13 cmg = 9.81 m/s²
T = s
2.Easy
3.3 kgk = 10 N/m

A 3.3 kg mass on a spring with stiffness 10 N/m oscillates on a frictionless surface. Find the period T.

m = 3.3 kgk = 10 N/m
T = s
3.Medium
2.6 kgk = 390 N/mA = 16 cmx = 10 cm

A 2.6 kg mass on a spring with k = 390 N/m oscillates on a frictionless surface with an amplitude of 16 cm. Find its speed v when it is 10 cm from equilibrium.

m = 2.6 kgk = 390 N/mA = 16 cmx = 10 cm
v = m/s
4.Medium
L = 2 mT = 4.61 s

An astronaut on another planet finds that a simple pendulum 2 m long has a period of 4.61 s for small swings. Find the gravitational acceleration g on that planet.

L = 2 mT = 4.61 s
g = m/s²
5.Hard
2.8 kgk = 90 N/mA = 9 cm

A 2.8 kg mass on a spring with k = 90 N/m is pulled 9 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.8 kgk = 90 N/mA = 9 cm
E = J
6.Hard
0.2 kgk = 440 N/mA = 7 cm

A 0.2 kg mass on a spring with k = 440 N/m is pulled 7 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.2 kgk = 440 N/mA = 7 cm
vmax = m/s

Answer key

  1. 1. T = 0.7233 s
  2. 2. T = 3.609 s
  3. 3. v = 1.53 m/s
  4. 4. g = 3.715 m/s²
  5. 5. E = 0.3645 J
  6. 6. vmax = 3.283 m/s

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