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
0.5 kgk25 cm

Hanging a 0.5 kg mass on a spring stretches it by 25 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 = 0.5 kgx = 25 cmg = 9.81 m/s²
T = s
2.Easy
0.8 kgk = 200 N/m

A 0.8 kg mass on a spring with stiffness 200 N/m oscillates on a frictionless surface. Find the period T.

m = 0.8 kgk = 200 N/m
T = s
3.Medium
L = 0.6 mT = 3.82 s

An astronaut on another planet finds that a simple pendulum 0.6 m long has a period of 3.82 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.6 mT = 3.82 s
g = m/s²
4.Medium
L = 1.6 mT = 2.67 s

An astronaut on another planet finds that a simple pendulum 1.6 m long has a period of 2.67 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.6 mT = 2.67 s
g = m/s²
5.Hard
1.5 kgk = 200 N/m100 m/s

A 15 g bullet moving at 100 m/s hits and stays in a 1.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 200 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 100 m/sM = 1.5 kgk = 200 N/m
A = cm
6.Hard
3.7 kgk = 210 N/mA = 12 cm

A 3.7 kg mass on a spring with k = 210 N/m is pulled 12 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.7 kgk = 210 N/mA = 12 cm
amax = m/s²

Answer key

  1. 1. T = 1.003 s
  2. 2. T = 0.3974 s
  3. 3. g = 1.623 m/s²
  4. 4. g = 8.86 m/s²
  5. 5. A = 8.617 cm
  6. 6. amax = 6.811 m/s²

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