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
1.4 kgk = 40 N/m

A 1.4 kg mass on a spring with stiffness 40 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.4 kgk = 40 N/m
f = Hz
2.Easy
4.4 kgk = ?

A 4.4 kg mass on a spring oscillates with a period of 1.15 s. Find the spring stiffness k.

m = 4.4 kgT = 1.15 s
k = N/m
3.Medium
L = 1.6 m

A simple pendulum has a length of 1.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.6 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.4 s? Use g = 9.81 m/s². Find L.

T = 2.4 sg = 9.81 m/s²
L = m
5.Hard
2.5 kgk = 400 N/mA = 17 cm

A 2.5 kg mass on a spring with k = 400 N/m is pulled 17 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.5 kgk = 400 N/mA = 17 cm
E = J
6.Hard
0.2 kgk = 20 N/mA = 12 cm

A 0.2 kg mass on a spring with k = 20 N/m is pulled 12 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.2 kgk = 20 N/mA = 12 cm
amax = m/s²

Answer key

  1. 1. f = 0.8507 Hz
  2. 2. k = 131.3 N/m
  3. 3. T = 2.537 s
  4. 4. L = 1.431 m
  5. 5. E = 5.78 J
  6. 6. amax = 12 m/s²

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