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
3.1 kgk = 100 N/m

A 3.1 kg mass on a spring with stiffness 100 N/m oscillates on a frictionless surface. Find the period T.

m = 3.1 kgk = 100 N/m
T = s
2.Easy
4.1 kgk = 20 N/m

A 4.1 kg mass on a spring with stiffness 20 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.1 kgk = 20 N/m
f = Hz
3.Medium
L = 3 m

A simple pendulum has a length of 3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 3 mg = 9.81 m/s²
T = s
4.Medium
L = 1.1 m

A simple pendulum has a length of 1.1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.1 mg = 9.81 m/s²
T = s
5.Hard
1 kgk = 40 N/mA = 20 cm

A 1 kg mass on a spring with k = 40 N/m is pulled 20 cm from equilibrium and released. Find its maximum speed vmax.

m = 1 kgk = 40 N/mA = 20 cm
vmax = m/s
6.Hard
0.2 kgk = 380 N/mA = 16 cm

A 0.2 kg mass on a spring with k = 380 N/m is pulled 16 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.2 kgk = 380 N/mA = 16 cm
amax = m/s²

Answer key

  1. 1. T = 1.106 s
  2. 2. f = 0.3515 Hz
  3. 3. T = 3.475 s
  4. 4. T = 2.104 s
  5. 5. vmax = 1.265 m/s
  6. 6. amax = 304 m/s²

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