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
1.6 kgk21 cm

Hanging a 1.6 kg mass on a spring stretches it by 21 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 1.6 kgx = 21 cmg = 9.81 m/s²
T = s
2.Easy
2.7 kgk = 350 N/m

A 2.7 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 2.7 kgk = 350 N/m
T = s
3.Medium
L = 0.4 m

A simple pendulum has a length of 0.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.4 mg = 9.81 m/s²
T = s
4.Medium
L = 1.2 m

A simple pendulum has a length of 1.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.2 mg = 9.81 m/s²
T = s
5.Hard
1 kgk = 1100 N/m400 m/s

An 8 g bullet moving at 400 m/s hits and stays in a 1 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1100 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 400 m/sM = 1 kgk = 1100 N/m
A = cm
6.Hard
2.4 kgk = 60 N/mA = 6 cm

A 2.4 kg mass on a spring with k = 60 N/m is pulled 6 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.4 kgk = 60 N/mA = 6 cm
amax = m/s²

Answer key

  1. 1. T = 0.9193 s
  2. 2. T = 0.5519 s
  3. 3. T = 1.269 s
  4. 4. T = 2.198 s
  5. 5. A = 9.61 cm
  6. 6. amax = 1.5 m/s²

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