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
3.9 kgk = 360 N/m

A 3.9 kg mass on a spring with stiffness 360 N/m oscillates on a frictionless surface. Find the period T.

m = 3.9 kgk = 360 N/m
T = s
2.Easy
0.6 kgk = 20 N/m

A 0.6 kg mass on a spring with stiffness 20 N/m oscillates on a frictionless surface. Find the period T.

m = 0.6 kgk = 20 N/m
T = s
3.Medium
L = 1.6 mT = 4.12 s

An astronaut on another planet finds that a simple pendulum 1.6 m long has a period of 4.12 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.6 mT = 4.12 s
g = m/s²
4.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
5.Hard
mk = 480 N/mA = 14 cmx = 6 cm

A mass on a spring with k = 480 N/m oscillates on a frictionless surface with an amplitude of 14 cm. Find its kinetic energy K when it is 6 cm from equilibrium.

k = 480 N/mA = 14 cmx = 6 cm
K = J
6.Hard
3.7 kgk = 240 N/mA = 3 cm

A 3.7 kg mass on a spring with k = 240 N/m is pulled 3 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.7 kgk = 240 N/mA = 3 cm
vmax = m/s

Answer key

  1. 1. T = 0.654 s
  2. 2. T = 1.088 s
  3. 3. g = 3.721 m/s²
  4. 4. T = 2.691 s
  5. 5. K = 3.84 J
  6. 6. vmax = 0.2416 m/s

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