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 = 20 N/m

A 4.3 kg mass on a spring with stiffness 20 N/m oscillates on a frictionless surface. Find the period T.

m = 4.3 kgk = 20 N/m
T = s
2.Easy
0.2 kgk = 300 N/m

A 0.2 kg mass on a spring with stiffness 300 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.2 kgk = 300 N/m
f = Hz
3.Medium
L = 0.2 m

A simple pendulum has a length of 0.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.2 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.6 s? Use g = 9.81 m/s². Find L.

T = 2.6 sg = 9.81 m/s²
L = m
5.Hard
3.4 kgk = 200 N/mA = 9 cm

A 3.4 kg mass on a spring with k = 200 N/m is pulled 9 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.4 kgk = 200 N/mA = 9 cm
E = J
6.Hard
0.3 kgk = 410 N/mA = 16 cm

A 0.3 kg mass on a spring with k = 410 N/m is pulled 16 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.3 kgk = 410 N/mA = 16 cm
amax = m/s²

Answer key

  1. 1. T = 2.913 s
  2. 2. f = 6.164 Hz
  3. 3. T = 0.8971 s
  4. 4. L = 1.68 m
  5. 5. E = 0.81 J
  6. 6. amax = 218.7 m/s²

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