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
0.4 kgk

A 0.4 kg mass on a spring makes 30 complete oscillations in 16 s. Find the frequency f of the oscillation.

m = 0.4 kgN = 30t = 16 s
f = Hz
2.Easy
3.8 kgk = 330 N/m

A 3.8 kg mass on a spring with stiffness 330 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.8 kgk = 330 N/m
f = Hz
3.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
4.Medium
L = 2.2 m

A simple pendulum has a length of 2.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.2 mg = 9.81 m/s²
T = s
5.Hard
2.2 kgk = 220 N/mA = 7 cm

A 2.2 kg mass on a spring with k = 220 N/m is pulled 7 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.2 kgk = 220 N/mA = 7 cm
vmax = m/s
6.Hard
3.2 kgk = 460 N/mA = 4 cm

A 3.2 kg mass on a spring with k = 460 N/m is pulled 4 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.2 kgk = 460 N/mA = 4 cm
E = J

Answer key

  1. 1. f = 1.875 Hz
  2. 2. f = 1.483 Hz
  3. 3. L = 1.431 m
  4. 4. T = 2.975 s
  5. 5. vmax = 0.7 m/s
  6. 6. E = 0.368 J

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