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
4.5 kgk = 120 N/m

A 4.5 kg mass on a spring with stiffness 120 N/m oscillates on a frictionless surface. Find the period T.

m = 4.5 kgk = 120 N/m
T = s
2.Easy
3.3 kgk = 170 N/m

A 3.3 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the period T.

m = 3.3 kgk = 170 N/m
T = s
3.Medium
L = 2.3 m

A simple pendulum has a length of 2.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.3 mg = 9.81 m/s²
T = s
4.Medium
1.1 kgk = 90 N/mA = 18 cmx = 5 cm

A 1.1 kg mass on a spring with k = 90 N/m oscillates on a frictionless surface with an amplitude of 18 cm. Find its speed v when it is 5 cm from equilibrium.

m = 1.1 kgk = 90 N/mA = 18 cmx = 5 cm
v = m/s
5.Hard
3.1 kgk = 400 N/mA = 18 cm

A 3.1 kg mass on a spring with k = 400 N/m is pulled 18 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.1 kgk = 400 N/mA = 18 cm
E = J
6.Hard
2.5 kgk = 500 N/mA = 8 cm

A 2.5 kg mass on a spring with k = 500 N/m is pulled 8 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.5 kgk = 500 N/mA = 8 cm
E = J

Answer key

  1. 1. T = 1.217 s
  2. 2. T = 0.8754 s
  3. 3. T = 3.042 s
  4. 4. v = 1.564 m/s
  5. 5. E = 6.48 J
  6. 6. E = 1.6 J

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