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
3.3 kgk = 230 N/m

A 3.3 kg mass on a spring with stiffness 230 N/m oscillates on a frictionless surface. Find the period T.

m = 3.3 kgk = 230 N/m
T = s
2.Easy
2.5 kgk = 180 N/m

A 2.5 kg mass on a spring with stiffness 180 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.5 kgk = 180 N/m
f = Hz
3.Medium
L = 1.9 m

A simple pendulum has a length of 1.9 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.9 mg = 9.81 m/s²
T = s
4.Medium
L = 2 mT = 6.98 s

An astronaut on another planet finds that a simple pendulum 2 m long has a period of 6.98 s for small swings. Find the gravitational acceleration g on that planet.

L = 2 mT = 6.98 s
g = m/s²
5.Hard
3.1 kgk = 110 N/mA = 13 cm

A 3.1 kg mass on a spring with k = 110 N/m is pulled 13 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.1 kgk = 110 N/mA = 13 cm
amax = m/s²
6.Hard
2.4 kgk = 210 N/m

A 2.4 kg mass is attached to the lower end of an unstretched vertical spring with k = 210 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2.4 kgk = 210 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. T = 0.7526 s
  2. 2. f = 1.35 Hz
  3. 3. T = 2.765 s
  4. 4. g = 1.621 m/s²
  5. 5. amax = 4.613 m/s²
  6. 6. vmax = 1.049 m/s

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