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
4.3 kgk = ?

A 4.3 kg mass on a spring oscillates with a period of 2.35 s. Find the spring stiffness k.

m = 4.3 kgT = 2.35 s
k = N/m
2.Easy
4.4 kgk = ?

A 4.4 kg mass on a spring oscillates with a period of 1 s. Find the spring stiffness k.

m = 4.4 kgT = 1 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.3 s? Use g = 9.81 m/s². Find L.

T = 2.3 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.5 s? Use g = 9.81 m/s². Find L.

T = 2.5 sg = 9.81 m/s²
L = m
5.Hard
0.8 kgk = 220 N/m

A 0.8 kg mass is attached to the lower end of an unstretched vertical spring with k = 220 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 0.8 kgk = 220 N/mg = 9.81 m/s²
xmax = cm
6.Hard
0.7 kgk = 460 N/mA = 17 cm

A 0.7 kg mass on a spring with k = 460 N/m is pulled 17 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.7 kgk = 460 N/mA = 17 cm
E = J

Answer key

  1. 1. k = 30.74 N/m
  2. 2. k = 173.7 N/m
  3. 3. L = 1.315 m
  4. 4. L = 1.553 m
  5. 5. xmax = 7.135 cm
  6. 6. E = 6.647 J

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