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
2.9 kgk = ?14.5 cm

Hanging a 2.9 kg mass on a spring stretches it by 14.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.9 kgx = 14.5 cmg = 9.81 m/s²
k = N/m
2.Easy
3.5 kgk = 100 N/m

A 3.5 kg mass on a spring with stiffness 100 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.5 kgk = 100 N/m
f = Hz
3.Medium
L = 1.5 m

A simple pendulum has a length of 1.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.5 mg = 9.81 m/s²
T = s
4.Medium
L = 0.9 mT = 2 s

An astronaut on another planet finds that a simple pendulum 0.9 m long has a period of 2 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.9 mT = 2 s
g = m/s²
5.Hard
0.6 kgk = 50 N/m

A 0.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 50 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 0.6 kgk = 50 N/mg = 9.81 m/s²
xmax = cm
6.Hard
mk = 270 N/mA = 8 cmx = 4 cm

A mass on a spring with k = 270 N/m oscillates on a frictionless surface with an amplitude of 8 cm. Find the energy U stored in the spring when the mass is 4 cm from equilibrium.

k = 270 N/mA = 8 cmx = 4 cm
U = J

Answer key

  1. 1. k = 196.2 N/m
  2. 2. f = 0.8507 Hz
  3. 3. T = 2.457 s
  4. 4. g = 8.883 m/s²
  5. 5. xmax = 23.54 cm
  6. 6. U = 0.216 J

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