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
1.8 kgk = 290 N/m

A 1.8 kg mass on a spring with stiffness 290 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.8 kgk = 290 N/m
f = Hz
2.Easy
0.8 kgk11.5 cm

Hanging a 0.8 kg mass on a spring stretches it by 11.5 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 = 0.8 kgx = 11.5 cmg = 9.81 m/s²
T = s
3.Medium
L = 0.5 mT = 2.3 s

An astronaut on another planet finds that a simple pendulum 0.5 m long has a period of 2.3 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.5 mT = 2.3 s
g = m/s²
4.Medium
L = 1.3 mT = 3.71 s

An astronaut on another planet finds that a simple pendulum 1.3 m long has a period of 3.71 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.3 mT = 3.71 s
g = m/s²
5.Hard
2.7 kgk = 350 N/mA = 14 cm

A 2.7 kg mass on a spring with k = 350 N/m is pulled 14 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.7 kgk = 350 N/mA = 14 cm
amax = m/s²
6.Hard
1.6 kgk = 120 N/m

A 1.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 120 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 1.6 kgk = 120 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. f = 2.02 Hz
  2. 2. T = 0.6803 s
  3. 3. g = 3.731 m/s²
  4. 4. g = 3.729 m/s²
  5. 5. amax = 18.15 m/s²
  6. 6. xmax = 26.16 cm

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