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 kgk = ?

A 1.2 kg mass on a spring makes 15 complete oscillations in 36 s. Find the spring stiffness k.

m = 1.2 kgN = 15t = 36 s
k = N/m
2.Easy
1.6 kgk = 90 N/m

A 1.6 kg mass on a spring with stiffness 90 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.6 kgk = 90 N/m
f = Hz
3.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
4.Medium
L = 2.5 m

A simple pendulum has a length of 2.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.5 mg = 9.81 m/s²
T = s
5.Hard
1.8 kgk = 500 N/mA = 15 cm

A 1.8 kg mass on a spring with k = 500 N/m is pulled 15 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.8 kgk = 500 N/mA = 15 cm
E = J
6.Hard
1.3 kgk = 50 N/mA = 17 cm

A 1.3 kg mass on a spring with k = 50 N/m is pulled 17 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.3 kgk = 50 N/mA = 17 cm
E = J

Answer key

  1. 1. k = 8.225 N/m
  2. 2. f = 1.194 Hz
  3. 3. L = 1.553 m
  4. 4. T = 3.172 s
  5. 5. E = 5.625 J
  6. 6. E = 0.7225 J

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