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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
4.6 kgk = 70 N/m

A 4.6 kg mass on a spring with stiffness 70 N/m oscillates on a frictionless surface. Find the period T.

m = 4.6 kgk = 70 N/m
T = s
2.Easy
1.8 kgk9 cm

Hanging a 1.8 kg mass on a spring stretches it by 9 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 = 1.8 kgx = 9 cmg = 9.81 m/s²
T = s
3.Medium
L = 1 mT = 3.26 s

An astronaut on another planet finds that a simple pendulum 1 m long has a period of 3.26 s for small swings. Find the gravitational acceleration g on that planet.

L = 1 mT = 3.26 s
g = m/s²
4.Medium
L = 2.4 m

A simple pendulum has a length of 2.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.4 mg = 9.81 m/s²
T = s
5.Hard
0.9 kgk = 20 N/mA = 15 cm

A 0.9 kg mass on a spring with k = 20 N/m is pulled 15 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.9 kgk = 20 N/mA = 15 cm
amax = m/s²
6.Hard
mk = 270 N/mA = 9 cmx = 7 cm

A mass on a spring with k = 270 N/m oscillates on a frictionless surface with an amplitude of 9 cm. Find the energy U stored in the spring when the mass is 7 cm from equilibrium.

k = 270 N/mA = 9 cmx = 7 cm
U = J

Answer key

  1. 1. T = 1.611 s
  2. 2. T = 0.6018 s
  3. 3. g = 3.715 m/s²
  4. 4. T = 3.108 s
  5. 5. amax = 3.333 m/s²
  6. 6. U = 0.6615 J

Full step-by-step solutions: practise this topic on examproblems.com.