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
1.6 kgk = ?

A 1.6 kg mass on a spring oscillates with a period of 0.45 s. Find the spring stiffness k.

m = 1.6 kgT = 0.45 s
k = N/m
2.Easy
3.4 kgk = ?

A 3.4 kg mass on a spring oscillates with a period of 2.25 s. Find the spring stiffness k.

m = 3.4 kgT = 2.25 s
k = N/m
3.Medium
L = 1.4 m

A simple pendulum has a length of 1.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.4 mg = 9.81 m/s²
T = s
4.Medium
L = 0.7 m

A simple pendulum has a length of 0.7 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.7 mg = 9.81 m/s²
T = s
5.Hard
0.6 kgk = 190 N/mA = 3 cm

A 0.6 kg mass on a spring with k = 190 N/m is pulled 3 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.6 kgk = 190 N/mA = 3 cm
E = J
6.Hard
1.8 kgk = 210 N/m

A 1.8 kg mass is attached to the lower end of an unstretched vertical spring with k = 210 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 1.8 kgk = 210 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. k = 311.9 N/m
  2. 2. k = 26.51 N/m
  3. 3. T = 2.374 s
  4. 4. T = 1.678 s
  5. 5. E = 0.0855 J
  6. 6. xmax = 16.82 cm

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